Patrick L. Combettes

Biography

Editorial boards

• Journal of Approximation Theory, 2008-present
• Journal of Mathematical Analysis and Applications, 2013-present
• Applied Mathematics and Optimization, 2022-present
• SIAM Journal on Mathematics of Data Science, 2019-present
• Numerical Algorithms, 2018-present
• Journal of Nonsmooth Analysis and Optimization, 2019-present
• SIAM Journal on Imaging Sciences, 2016-2025
• SIAM Journal on Optimization, 2007-2019
• IEEE Transactions on Image Processing, 1997-2002

Scientific awards

• SIAM Fellow, 2024
  For contributions to the theory and applications of convex optimization, especially proximal methods
• IEEE Fellow, 2005
  For contributions to set-theoretic methods and convex analysis in signal and image processing
• Best Paper Award, IEEE Signal Processing Society, 1993

Administrative positions

• Founding director (2009-2013) of the CNRS research consortium MOA on mathematical optimization and its applications.

Academic positions

• North Carolina State University, 2016-present
  Department of Mathematics
  8/2016: Distinguished Professor

• Université Pierre et Marie Curie – Paris 6, 1999-2016
  Laboratoire Jacques-Louis Lions, Faculté de Mathématiques
  9/2010: Professeur, classe exceptionnelle (CNU)
  9/2003: Professeur, première classe (CNU)
  9/1999: Professeur, deuxième classe

• City University of New York, 1990-1999
  City College and Graduate Center
  1/1999: Full Professor
  1/1994: Associate Professor
  9/1990: Assistant Professor

Publications

[PRx] [Bx] [Dx] [Jx] [Ex] [Cx] [Sx]

Preprint Book Edited book Journal article Book chapter Conference proceedings paper Guest edition of a special issue of a journal

Preprints

[PR2]

P. L. Combettes, La méthode du gradient proximé. [arXiv]

[PR1]

P. L. Combettes and J. I. Madariaga, Almost-surely convergent randomly activated monotone operator splitting methods. [arXiv]

2025

[J111]

P. L. Combettes and D. J. Cornejo, Variational analysis of proximal compositions and integral proximal mixtures, Evolution Equations and Control Theory, to appear. [pdf]

[J110]

M. N. Bùi and P. L. Combettes, Interchange rules for integral functions, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, to appear. [pdf]

[J109]

M. N. Bùi and P. L. Combettes, Hilbert direct integrals of monotone operators, Canadian Journal of Mathematics, to appear. [pdf]

[J108]

L. M. Briceño-Arias, P. L. Combettes, and F. J. Silva, Perspective functions with nonlinear scaling, Communications in Contemporary Mathematics, vol. 27, no. 1, art. 2350065 (37 pp.), January 2025. [pdf]

2024

[J107]

M. N. Bùi and P. L. Combettes, Integral resolvent and proximal mixtures, Journal of Optimization Theory and Applications, vol. 203, no. 3, pp. 2328–2353, December 2024. [pdf]

[J106]

L. M. Briceño-Arias, P. L. Combettes, and F. J. Silva, Proximity operators of perspective functions with nonlinear scaling, SIAM Journal on Optimization, vol. 34, no. 4, pp. 3212–3234, October 2024. [pdf]

[J105]

P. L. Combettes, The geometry of monotone operator splitting methods, Acta Numerica, vol. 33, pp. 487–632, September 2024. [pdf]

[J104]

L. M. Briceño-Arias and P. L. Combettes, A perturbation framework for convex minimization and monotone inclusion problems with nonlinear compositions, Mathematics of Operations Research, vol. 49, no. 3, pp. 1890–1914, August 2024. [pdf]

[C64]

P. L. Combettes and J. I. Madariaga, Randomly activated proximal methods for nonsmooth convex minimization, Proceedings of the European Signal Processing Conference, pp. 2642–2646. Lyon, France, August 26–30, 2024.

[C63]

P. L. Combettes and D. J. Cornejo, Signal recovery with proximal comixtures, Proceedings of the European Signal Processing Conference, pp. 2637–2641. Lyon, France, August 26–30, 2024. [pdf]

2023

[J103]

P. L. Combettes, Resolvent and proximal compositions, Set-Valued and Variational Analysis, vol. 31, no. 3, art. 22, 29 pp., September 2023. [pdf]

[C62]

P. L. Combettes, J.-C. Pesquet, and A. Repetti, A variational inequality model for learning neural networks, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 5 pp. Rhodes Island, Greece, June 4–10, 2023. [pdf]

2022

[J102]

M. N. Bùi and P. L. Combettes, Analysis and numerical solution of a modular convex Nash equilibrium problem, Journal of Convex Analysis, vol. 29, no. 4, pp. 1007–1021, December 2022. [pdf]

[J101]

M. N. Bùi and P. L. Combettes, Multivariate monotone inclusions in saddle form, Mathematics of Operations Research, vol. 47, no. 2, pp. 1082–1109, May 2022. [pdf]

[J100]

P. L. Combettes and Z. C. Woodstock, A variational inequality model for the construction of signals from inconsistent nonlinear equations, SIAM Journal on Imaging Sciences, vol. 15, no. 1, pp. 84–109, January 2022. [pdf]

[C61]

M. N. Bùi, P. L. Combettes, and Z. C. Woodstock, Block-activated algorithms for multicomponent fully nonsmooth minimization, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 5428–5432. Singapore, May 22–27, 2022. [pdf]

[C60]

P. L. Combettes and Z. C. Woodstock, Signal recovery from inconsistent nonlinear observations, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 5872–5876. Singapore, May 22–27, 2022.

2021

[J99]

M. N. Bùi and P. L. Combettes, Bregman forward-backward operator splitting, Set-Valued and Variational Analysis, vol. 29, no. 3, pp. 583–603, September 2021. [pdf]

[J98]

P. L. Combettes and J.-C. Pesquet, Fixed point strategies in data science, IEEE Transactions on Signal Processing, vol. 69, pp. 3878–3905, August 2021. [pdf]

[J97]

P. L. Combettes and Z. C. Woodstock, Reconstruction of functions from prescribed proximal points, Journal of Approximation Theory, vol. 268, art. 105606, 26 pp., August 2021. [pdf]

[J96]

P. L. Combettes and C. L. Müller, Regression models for compositional data: General log-contrast formulations, proximal optimization, and microbiome data applications, Statistics in Biosciences, vol. 13, no. 2, pp. 217–242, July 2021. [pdf]

[J95]

P. L. Combettes and L. E. Glaudin, Solving composite fixed point problems with block updates, Advances in Nonlinear Analysis, vol. 10, pp. 1154–1177, March 2021. [pdf]

[C59]

P. L. Combettes and Z. C. Woodstock, A fixed point framework for recovering signals from nonlinear transformations, Proceedings of the European Signal Processing Conference, pp. 2120–2124. Amsterdam, The Netherlands, January 18–22, 2021. [pdf]

2020

[J94]

M. N. Bùi and P. L. Combettes, Warped proximal iterations for monotone inclusions, Journal of Mathematical Analysis and Applications, vol. 491, no. 1, art. 124315, 21 pp., November 2020. [pdf]

[J93]

P. L. Combettes and J.-C. Pesquet, Deep neural network structures solving variational inequalities, Set-Valued and Variational Analysis, vol. 28, no. 3, pp. 491–518, September 2020. [pdf]

[J92]

P. L. Combettes and J.-C. Pesquet, Lipschitz certificates for layered network structures driven by averaged activation operators, SIAM Journal on Mathematics of Data Science, vol. 2, no. 2, pp. 529–557, June 2020. [pdf]

[J91]

M. N. Bùi and P. L. Combettes, The Douglas-Rachford algorithm converges only weakly, SIAM Journal on Control and Optimization, vol. 58, no. 2, pp. 1118–1120, April 2020. [pdf]

[J90]

P. L. Combettes and C. L. Müller, Perspective maximum likelihood-type estimation via proximal decomposition, Electronic Journal of Statistics, vol. 14, no. 1, pp. 207–238, January 2020. [pdf]

2019

[J89]

P. L. Combettes and L. E. Glaudin, Proximal activation of smooth functions in splitting algorithms for convex image recovery, SIAM Journal on Imaging Sciences, vol. 12, no. 4, pp. 1905–1935, November 2019. [pdf]

[J88]

P. L. Combettes, A. M. McDonald, C. A. Micchelli, and M. Pontil, Learning with optimal interpolation norms, Numerical Algorithms, vol. 81, no. 2, pp. 695–717, June 2019. [pdf]

[J87]

P. L. Combettes and J.-C. Pesquet, Stochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping II: Mean-square and linear convergence, Mathematical Programming, vol. B174, no. 1, pp. 433–451, April 2019. [pdf]

[C58]

P. L. Combettes and L. E. Glaudin, Fully proximal splitting algorithms in image recovery, Proceedings of the European Signal Processing Conference, pp. 525-529. A Coruña, Spain, September 2–6, 2019.

2018

[J86]

P. L. Combettes, Monotone operator theory in convex optimization, Mathematical Programming, vol. B170, no. 1, pp. 177–206, July 2018. [pdf]

[J85]

P. L. Combettes, Perspective functions: Properties, constructions, and examples, Set-Valued and Variational Analysis, vol. 26, no. 2, pp. 247–264, June 2018. [pdf]

[J84]

P. L. Combettes and J. Eckstein, Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions, Mathematical Programming, vol. B168, no. 1, pp. 645–672, March 2018. [pdf]

[J83]

P. L. Combettes and C. L. Müller, Perspective functions: Proximal calculus and applications in high-dimensional statistics, Journal of Mathematical Analysis and Applications, vol. 457, no. 2, pp. 1283–1306, January 2018. [pdf]

[J82]

P. L. Combettes, S. Salzo, and S. Villa, Regularized learning schemes in feature Banach spaces, Analysis and Applications, vol. 16, no. 1, pp. 1–54, January 2018. [pdf]

[J81]

P. L. Combettes, S. Salzo, and S. Villa, Consistent learning by composite proximal thresholding, Mathematical Programming, vol. B167, no. 1, pp. 99–127, January 2018. [pdf]

[C57]

P. L. Combettes and J.-C. Pesquet, Linear convergence of stochastic block-coordinate fixed point algorithms, Proceedings of the European Signal Processing Conference, pp. 747–751. Rome, Italy, September 3–7, 2018.

2017

[B02]

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, second edition. Springer, New York, 2017. [pdf]

[J80]

P. L. Combettes and L. E. Glaudin, Quasinonexpansive iterations on the affine hull of orbits: From Mann's mean value algorithm to inertial methods, SIAM Journal on Optimization, vol. 27, no. 4, pp. 2356–2380, December 2017. [pdf]

[J79]

M. Barlaud, W. Belhajali, P. L. Combettes, and L. Fillatre, Classification and regression using an outer approximation projection-gradient method, IEEE Transactions on Signal Processing, vol. 65, no. 17, pp. 4635–4644, September 2017. [pdf]

2016

[J78]

H. Attouch, L. M. Briceño-Arias, and P. L. Combettes, A strongly convergent primal-dual method for nonoverlapping domain decomposition, Numerische Mathematik, vol. 133, no. 3, pp. 433–470, July 2016. [pdf]

[J77]

P. L. Combettes and Q. V. Nguyen, Solving composite monotone inclusions in reflexive Banach spaces by constructing best Bregman approximations from their Kuhn-Tucker set, Journal of Convex Analysis, vol. 23, no. 2, pp. 481–510, May 2016. Special issue dedicated to the memory of Jean Jacques Moreau. [pdf]

[J76]

P. L. Combettes and Đinh Dũng, Kolmogorov n-widths of function classes induced by a non-degenerate differential operator: A convex duality approach, Set-Valued and Variational Analysis, vol. 24, no. 1, pp. 83–99, March 2016. [pdf]

[J75]

P. L. Combettes and J.-C. Pesquet, Stochastic approximations and perturbations in forward-backward splitting for monotone operators, Pure and Applied Functional Analysis, vol. 1, no. 1, pp. 13–37, January 2016. [pdf]

[C56]

P. L. Combettes and J.-C. Pesquet, Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration, Proceedings of the European Signal Processing Conference, 5 pages. Budapest, Hungary, August 29-September 3, 2016. [pdf]

2015

[J74]

A. Alotaibi, P. L. Combettes, and N. Shahzad, Best approximation from the Kuhn-Tucker set of composite monotone inclusions, Numerical Functional Analysis and Optimization, vol. 36, no. 12, pp. 1513–1532, December 2015. [pdf]

[J73]

P. L. Combettes and J.-C. Pesquet, Stochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping, SIAM Journal on Optimization, vol. 25, no. 2, pp. 1221–1248, July 2015. [pdf]

[J72]

P. L. Combettes and I. Yamada, Compositions and convex combinations of averaged nonexpansive operators, Journal of Mathematical Analysis and Applications, vol. 425, no. 1, pp. 55–70, May 2015. [pdf]

2014

[S01]

P. L. Combettes, J.-B. Hiriart-Urruty, and M. Théra (Guest editors), Modern convex analysis, Mathematical Programming, vol. B148, nos. 1–2, December 2014. [pdf]

[J71]

A. Alotaibi, P. L. Combettes, and N. Shahzad, Solving coupled composite monotone inclusions by successive Fejér approximations of their Kuhn-Tucker set, SIAM Journal on Optimization, vol. 24, no. 4, pp. 2076–2095, December 2014. [pdf]

[J70]

M. A. Alghamdi, A. Alotaibi, P. L. Combettes, and N. Shahzad, A primal-dual method of partial inverses for composite inclusions, Optimization Letters, vol. 8, no. 8, pp. 2271–2284, December 2014. [pdf]

[J69]

P. L. Combettes and B. C. Vũ, Variable metric forward-backward splitting with applications to monotone inclusions in duality, Optimization, vol. 63, no. 9, pp. 1289–1318, September 2014. [pdf] (published online 2012-12-13)

[J68]

J.-B. Baillon, P. L. Combettes, and R. Cominetti, Asymptotic behavior of compositions of under-relaxed nonexpansive operators, Journal of Dynamics and Games, vol. 1, no. 3, pp. 331–346, July 2014. [pdf]

[J67]

S. R. Becker and P. L. Combettes, An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery, Journal of Nonlinear and Convex Analysis, vol. 15, no. 1, pp. 137–159, January 2014. [pdf]

[C55]

P. L. Combettes, L. Condat, J.-C. Pesquet, and B. C. Vũ, A forward-backward view of some primal-dual optimization methods in image recovery, Proceedings of the IEEE International Conference on Image Processing. Paris, France, October 27–30, 2014. [pdf]

2013

[J66]

P. L. Combettes, Systems of structured monotone inclusions: Duality, algorithms, and applications, SIAM Journal on Optimization, vol. 23, no. 4, pp. 2420–2447, December 2013. [pdf]

[J65]

P. L. Combettes and N. N. Reyes, Moreau's decomposition in Banach spaces, Mathematical Programming, vol. 139, no. 1, pp. 103–114, June 2013. [pdf]

[J64]

P. L. Combettes and B. C. Vũ, Variable metric quasi-Fejér monotonicity, Nonlinear Analysis: Theory, Methods, and Applications, vol. 78, pp. 17–31, February 2013. [pdf]

[E05]

L. M. Briceño-Arias and P. L. Combettes, Monotone operator methods for Nash equilibria in non-potential games, in: Computational and Analytical Mathematics, (D. Bailey, H. H. Bauschke, P. Borwein, F. Garvan, M. Théra, J. Vanderwerff, and H. Wolkowicz, Editors), pp. 143–159. Springer, New York, 2013. [pdf]

2012

[J63]

P. L. Combettes and J.-C. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued and Variational Analysis, vol. 20, no. 2, pp. 307–330, June 2012. [pdf]

[J62]

Y. Censor, W. Chen, P. L. Combettes, R. Davidi, and G. T. Herman, On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Computational Optimization and Applications, vol. 51, no. 3, pp. 1065–1088, April 2012. [pdf]

[J61]

J.-B. Baillon, P. L. Combettes, and R. Cominetti, There is no variational characterization of the cycles in the method of periodic projections, Journal of Functional Analysis, vol. 262, no. 1, pp. 400–408, January 2012. [pdf]

2011

[B02]

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York, 2011. [pdf excerpt]

[J60]

L. M. Briceño-Arias and P. L. Combettes, A monotone+skew splitting model for composite monotone inclusions in duality, SIAM Journal on Optimization, vol. 21, no. 4, pp. 1230–1250, October 2011. [pdf]

[J59]

L. M. Briceño-Arias, P. L. Combettes, J.-C. Pesquet, and N. Pustelnik, Proximal algorithms for multicomponent image recovery problems, Journal of Mathematical Imaging and Vision, vol. 41, no. 1, pp. 3–22, September 2011. [pdf]

[J58]

P. L. Combettes, Đinh Dũng, and B. C. Vũ, Proximity for sums of composite functions, Journal of Mathematical Analysis and Applications, vol. 380, no. 2, pp. 680–688, August 2011. [pdf]

[E04]

P. L. Combettes and J.-C. Pesquet, Proximal splitting methods in signal processing, in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, (H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. R. Luke, and H. Wolkowicz, Editors), pp. 185–212. Springer, New York, 2011. [pdf]

[D01]

H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. R. Luke, and H. Wolkowicz (Editors), Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer, New York, 2011.

2010

[J57]

P. L. Combettes, Đinh Dũng, and B. C. Vũ, Dualization of signal recovery problems, Set-Valued and Variational Analysis, vol. 18, pp. 373–404, December 2010. [pdf]

[J56]

H. H. Bauschke and P. L. Combettes, The Baillon-Haddad theorem revisited, Journal of Convex Analysis, vol. 17, no. 4, pp. 781–787, December 2010. [pdf]

[J55]

P. L. Combettes and N. N. Reyes, Functions with prescribed best linear approximations, Journal of Approximation Theory, vol. 162, no. 5, pp. 1095–1116, May 2010. [pdf]

[J54]

H. Attouch, L. M. Briceño-Arias, and P. L. Combettes, A parallel splitting method for coupled monotone inclusions, SIAM Journal on Control and Optimization, vol. 48, no. 5, pp. 3246–3270, January 2010. [pdf]

[C54]

L. M. Briceño-Arias, P. L. Combettes, J.-C. Pesquet, and N. Pustelnik, Proximal method for geometry and texture image decomposition, Proceedings of the IEEE International Conference on Image Processing. Hong-Kong, September 26–29, 2010.

[C53]

J. Bolte, P. L. Combettes, and J.-C. Pesquet, Alternating proximal algorithm for blind image recovery, Proceedings of the IEEE International Conference on Image Processing. Hong-Kong, September 26–29, 2010. [pdf]

2009

[J53]

P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators, Journal of Convex Analysis, vol. 16, no. 4, pp. 727-748, December 2009. [pdf]

[J52]

L. M. Briceño-Arias and P. L. Combettes, Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery, Numerical Mathematics: Theory, Methods, and Applications, vol. 2, no. 4, pp. 485–508, November 2009. [pdf]

[C52]

P. L. Combettes and J.-C. Pesquet, Split convex minimization algorithm for signal recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 685–688. Taipei, Taiwan, April 19–24, 2009.

2008

[J51]

P. L. Combettes and J.-C. Pesquet, A proximal decomposition method for solving convex variational inverse problems, Inverse Problems, vol. 24, no. 6, article ID 065014, 27 pp., December 2008. [pdf]

[J50]

H. H. Bauschke and P. L. Combettes, A Dykstra-like algorithm for two monotone operators, Pacific Journal of Optimization, vol. 4, no. 3, pp. 383–391, September 2008. [pdf]

[J49]

P. L. Combettes and S. A. Hirstoaga, Visco-penalization of the sum of two monotone operators, Nonlinear Analysis: Theory, Methods, and Applications, vol. 69, no. 2, pp. 579–591, July 2008. [pdf]

2007

[J48]

P. L. Combettes and J.-C. Pesquet, A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery, IEEE Journal of Selected Topics in Signal Processing, vol. 1, no. 4, pp. 564–574, December 2007. [pdf]

[J47]

P. L. Combettes and J.-C. Pesquet, Proximal thresholding algorithm for minimization over orthonormal bases, SIAM Journal on Optimization, vol. 18, no. 4, pp. 1351–1376, November 2007. [pdf]

[J46]

C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, A variational formulation for frame-based inverse problems, Inverse Problems, vol. 23, no. 4, pp. 1495–1518, August 2007. [pdf]

[E03]

T. D. Capricelli and P. L. Combettes, A convex programming algorithm for noisy discrete tomography, in: Advances in Discrete Tomography and Its Applications, (G. T. Herman and A. Kuba, Editors), pp. 207–226. Boston, MA: Birkhäuser, 2007. [pdf]

[C51]

C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, Opérateurs proximaux pour la restauration bayésienne de signaux, Proceedings of the 21st GRETSI Symposium, pp. 1277–1280. Troyes, France, 11–14 Septembre 2007.

[C50]

P. L. Combettes and J.-C. Pesquet, Sparse signal recovery by iterative proximal thresholding, Proceedings of the 15th European Signal Processing Conference, 4 pages. Poznan, Poland, September 3–7, 2007.

2006

[J45]

P. L. Combettes and S. A. Hirstoaga, Approximating curves for nonexpansive and monotone operators, Journal of Convex Analysis, vol. 13, nos. 3–4, pp. 633–646, December 2006. [pdf]

[J44]

H. H. Bauschke, P. L. Combettes, and D. Noll, Joint minimization with alternating Bregman proximity operators, Pacific Journal of Optimization, vol. 2, no. 3, pp. 401–424, September 2006. [pdf]

[J43]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space, Journal of Approximation Theory, vol. 141, no. 1, pp. 63–69, July 2006. [pdf]

[J42]

H. H. Bauschke, P. L. Combettes, and S. G. Kruk, Extrapolation algorithm for affine-convex feasibility problems, Numerical Algorithms, vol. 41, no. 3, pp. 239–274, March 2006. [pdf]

[C49]

C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, Iterative image deconvolution using overcomplete representations, Proceedings of the 14th European Signal Processing Conference, 4 pages. Florence, Italy, September 4–8, 2006.

[C48]

H. H. Bauschke, P. L. Combettes, and J.-C. Pesquet, A decomposition method for nonsmooth convex variational signal recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 989–992. Toulouse, France, May 14–19, 2006.

2005

[J41]

P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Modeling and Simulation, vol. 4, no. 4, pp. 1168–1200, November 2005. [pdf]

[J40]

P. L. Combettes and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, April 2005. [pdf]

[J39]

H. H. Bauschke, P. L. Combettes, and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Analysis: Theory, Methods, and Applications, vol. 60, no. 2, pp. 283–301, January 2005. [pdf]

[C47]

C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, A forward-backward algorithm for image restoration with sparse representations, Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations, pp. 49–52. Rennes, France, November 16–18, 2005.

[C46]

T. D. Capricelli and P. L. Combettes, Éclatement des contraintes en reconstruction tomographique, Proceedings of the 20th GRETSI Symposium, pp. 655–658. Louvain-la-Neuve, Belgium, 6–9 Septembre 2005.

[C45]

T. D. Capricelli and P. L. Combettes, Parallel block-iterative reconstruction algorithms for binary tomography, Electronic Notes in Discrete Mathematics, vol. 20, pp. 263–280, July 2005.

[C44]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, A new generation of iterative transform algorithms for phase contrast tomography, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 89–92. Philadelphia, PA, March 19–23, 2005.

2004

[J38]

P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, vol. 53, no. 5–6, pp. 475–504, December 2004. [pdf]

[J37]

P. L. Combettes and J. C. Pesquet, Wavelet-constrained image restoration, International Journal of Wavelets, Multiresolution, and Information Processing, vol. 2, no. 4, pp. 371–389, December 2004. [pdf]

[J36]

P. L. Combettes and T. Pennanen, Proximal methods for cohypomonotone operators, SIAM Journal on Control and Optimization, vol. 43, no. 2, pp. 731–742, October 2004. [pdf]

[J35]

P. L. Combettes and J. C. Pesquet, Image restoration subject to a total variation constraint, IEEE Transactions on Image Processing, vol. 13, no. 9, pp. 1213–1222, September 2004. [pdf]

[J34]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, Finding best approximation pairs relative to two closed convex sets in Hilbert spaces, Journal of Approximation Theory, vol. 127, no. 2, pp. 178–192, March 2004. [pdf]

[C43]

P. L. Combettes and V. R. Wajs, Theoretical analysis of some regularized image denoising methods, Proceedings of the IEEE International Conference on Image Processing, vol. 1, pp. 969–972. Singapore, October 24–27, 2004.

[C42]

P. L. Combettes and J. C. Pesquet, Estimating first-order finite-difference information in image restoration problems, Proceedings of the IEEE International Conference on Image Processing, vol. 1, pp. 321–324. Singapore, October 24–27, 2004.

[C41]

P. L. Combettes and J. C. Pesquet, Constraint construction in convex set theoretic signal recovery via Stein's principle, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 813–816. Montréal, Canada, May 17–21, 2004.

2003

[J33]

H. H. Bauschke and P. L. Combettes, Construction of best Bregman approximations in reflexive Banach spaces, Proceedings of the American Mathematical Society, vol. 131, no. 12, pp. 3757–3766, December 2003. [pdf]

[J32]

P. L. Combettes, A block-iterative surrogate constraint splitting method for quadratic signal recovery, IEEE Transactions on Signal Processing, vol. 51, no. 7, pp. 1771–1782, July 2003. [pdf]

[J31]

H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Bregman monotone optimization algorithms, SIAM Journal on Control and Optimization, vol. 42, no. 2, pp. 596–636, June 2003. [pdf]

[J30]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, Hybrid projection-reflection method for phase retrieval, Journal of the Optical Society of America A, vol. 20, no. 6, pp. 1025–1034, June 2003. [pdf]

[J29]

H. H. Bauschke and P. L. Combettes, Iterating Bregman retractions, SIAM Journal on Optimization, vol. 13, no. 4, pp. 1159–1173, April 2003. [pdf]

[C40]

P. L. Combettes and J. C. Pesquet, Image deconvolution with total variation bounds, Proceedings of the Seventh International Symposium on Signal Processing and Its Applications, vol. 1, pp. 441–444. Paris, France, July 1–4, 2003.

[C39]

P. L. Combettes and J. C. Pesquet, Incorporating total variation information in image recovery, Proceedings of the IEEE International Conference on Image Processing, vol. 3, pp. 373–376. Barcelona, Spain, September 14–17, 2003.

2002

[J28]

P. L. Combettes and T. Pennanen, Generalized Mann iterates for constructing fixed points in Hilbert spaces, Journal of Mathematical Analysis and Applications, vol. 275, no. 2, pp. 521–536, November 2002. [pdf]

[J27]

P. L. Combettes and J. Luo, An adaptive level set method for nondifferentiable constrained image recovery, IEEE Transactions on Image Processing, vol. 11, no. 11, pp. 1295–1304, November 2002. [pdf]

[J26]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization, Journal of the Optical Society of America A, vol. 19, no. 7, pp. 1334–1345, July 2002. [pdf]

[C38]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, On the structure of some phase retrieval algorithms, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 841–844. Rochester, NY, September 22–25, 2002.

2001

[J25]

H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces, Communications in Contemporary Mathematics, vol. 3, no. 4, pp. 615–647, 2001. [pdf]

[J24]

H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces, Mathematics of Operations Research, vol. 26, no. 2, pp. 248–264, May 2001. [pdf]

[J23]

P. L. Combettes, On the numerical robustness of the parallel projection method in signal synthesis, IEEE Signal Processing Letters, vol. 8, no. 2, pp. 45–47, February 2001.

[E02]

P. L. Combettes, Quasi-Fejérian analysis of some optimization algorithms, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, (D. Butnariu, Y. Censor, and S. Reich, Eds.), pp. 115–152. New York: Elsevier, 2001. [pdf]

[E01]

P. L. Combettes, Fejér-monotonicity in convex optimization, in Encyclopedia of Optimization (C. A. Floudas and P. M. Pardalos, Eds.), vol. 2, pp. 106–114. Springer-Verlag, New York, 2001. [pdf]

[C37]

P. L. Combettes, Convex set theoretic image recovery with inexact projection algorithms, Proceedings of the IEEE International Conference on Image Processing, vol. 1, pp. 257–260. Thessaloniki, Greece, October 7–10, 2001.

[C36]

P. L. Combettes, Convexité et signal, Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01, pp. 6–16. Pompadour, France, May 28-June 1, 2001. [pdf]

2000

[J22]

P. L. Combettes, Strong convergence of block-iterative outer approximation methods for convex optimization, SIAM Journal on Control and Optimization , vol. 38, no. 2, pp. 538–565, February 2000. [pdf]

[C35]

P. L. Combettes, A parallel constraint disintegration and approximation scheme for quadratic signal recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 1, pp. 165–168. Istanbul, Turkey, June 5–9, 2000.

[C34]

J. Luo and P. L. Combettes, A level-set subgradient projection algorithm for non-differentiable signal restoration with multiple constraints, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 1, pp. 225–228. Istanbul, Turkey, June 5–9, 2000.

1999

[J21]

P. L. Combettes and P. Bondon, Hard-constrained inconsistent signal feasibility problems, IEEE Transactions on Signal Processing, vol. 47, no. 9, pp. 2460–2468, September 1999. [pdf]

[C33]

J. Luo and P. L. Combettes, A subgradient projection algorithm for nondifferentiable signal recovery, Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing, pp. 452–456. Antalya, Turkey, June 20–23, 1999.

1998

[J20]

P. L. Combettes and J. C. Pesquet, Convex multiresolution analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 12, pp. 1308–1318, December 1998. Gzipped PostScript

[C32]

P. L. Combettes and J. C. Pesquet, Nonlinear multiresolution image analysis via convex projections, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 762–765. Chicago, IL, October 4–7, 1998.

[C31]

P. L. Combettes and P. Bondon, Constrained pulse shape synthesis for digital communications, Proceedings of the European Signal Processing Conference, pp. 573–576. Island of Rhodes, Greece, September 8–11, 1998.

[C30]

P. L. Combettes, A block-iterative quadratic signal recovery algorithm, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 2917–2920. Seattle, WA, May 12–15, 1998.

1997

[J19]

P. L. Combettes, Hilbertian convex feasibility problem: Convergence of projection methods, Applied Mathematics and Optimization, vol. 35, no. 3, pp. 311–330, May 1997. [pdf]

[J18]

P. L. Combettes, Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections, IEEE Transactions on Image Processing, vol. 6, no. 4, pp. 493–506, April 1997. [pdf]

[C29]

P. L. Combettes and P. Bondon, Hard-constrained signal feasibility problems, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 2569–2572. Munich, Germany, April 21–24, 1997.

1996

[J17]

P. L. Combettes and T. J. Chaussalet, Combining statistical information in set theoretic estimation, IEEE Signal Processing Letters, vol. 3, no. 3, pp. 61–62, March 1996. [Gzipped PostScript]

[J16]

J. C. Pesquet and P. L. Combettes, Wavelet synthesis by alternating projections, IEEE Transactions on Signal Processing, vol. 44, no. 3, pp. 728–732, March 1996.

[B01]

P. L. Combettes, The Convex Feasibility Problem in Image Recovery, vol. 95 of Advances in Imaging and Electron Physics, Academic Press, New York, 1996. [pdf]

[C28]

P. L. Combettes, Generalized convex set theoretic image recovery, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 453–456. Lausanne, Switzerland, September 16–19, 1996.

[C27]

P. L. Combettes, Bounded-error models in inverse problems, Proceedings of the 1996 IMACS/IEEE MultiConference on Computational Engineering in Systems Applications, vol. 2, pp. 1023–1027. Lille, France, July 9–12, 1996.

[C26]

P. L. Combettes and J. C. Pesquet, Convex multiresolution analysis, Proceedings of the IEEE International Symposium on Time-Frequency and Time-Scale Analysis, pp. 301–304. Paris, France, June 18–21, 1996.

[C25]

H. Puh and P. L. Combettes, Operator theoretic image coding, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 1863–1866. Atlanta, GA, May 7–10, 1996.

[C24]

H. Puh and P. L. Combettes, Set theoretic vector quantization, Proceedings of the Ninth IEEE Workshop on Image and Multidimensional Signal Processing, pp. 48–49. Belize City, Belize, March 3–6, 1996.

1995

[J15]

P. Bondon, P. L. Combettes, and B. Picinbono, Volterra filtering and higher order whiteness, IEEE Transactions on Signal Processing, vol. 43, no. 9, pp. 2209–2212, September 1995. [Gzipped PostScript]

[J14]

P. L. Combettes, Construction d'un point fixe commun à une famille de contractions fermes, Comptes Rendus de l'Académie des Sciences de Paris, Série I (Mathématique) , vol. 320, no. 11, pp. 1385–1390, June 1995. [pdf]

[J13]

P. L. Combettes and H. J. Trussell, Deconvolution with bounded uncertainty, International Journal of Adaptive Control and Signal Processing, vol. 9, no. 1, pp. 3–17, January 1995. [pdf]

[C23]

P. L. Combettes, Constrained image recovery in a product space, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 25–28. Washington, DC, October 23–26, 1995.

[C22]

P. L. Combettes, Restauration ensembliste d'images par itérations parallèles extrapolées de sous-gradients, Proceedings of the 15th GRETSI Symposium, pp. 447–450. Juan-les-Pins, France, September 18–22, 1995.

[C21]

P. L. Combettes and P. Bondon, Adaptive linear filtering with convex constraints, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 1372–1375. Detroit, MI, May 8–12, 1995.

1994

[J12]

P. L. Combettes, Inconsistent signal feasibility problems: Least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol. 42, no. 11, pp. 2955–2966, November 1994. [pdf]

[J11]

P. L. Combettes and H. Puh, Iterations of parallel convex projections in Hilbert spaces, Numerical Functional Analysis and Optimization, vol. 15, nos. 3–4, pp. 225–243, 1994.

[C20]

P. L. Combettes, Convex set theoretic image recovery via chaotic iterations of approximate projections, Proceedings of the IEEE International Conference on Image Processing, vol. 3, pp. 182–186. Austin, TX, November 13–16, 1994.

[C19]

P. L. Combettes and T. J. Chaussalet, Selecting statistical information in set theoretic signal processing, Proceedings of the Seventh IEEE Workshop on Statistical Signal and Array Processing, pp. 55–58. Québec City, Canada, June 26–29, 1994.

[C18]

P. L. Combettes, Set theoretic signal processing, Proceedings of the Seventh IEEE Workshop on Statistical Signal and Array Processing, pp. 1–6. Québec City, Canada, June 26–29, 1994.

[C17]

P. L. Combettes and H. Puh, A fast parallel projection algorithm for set theoretic image recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 473–476. Adelaide, Australia, April 19–22, 1994.

[C16]

J. C. Pesquet and P. L. Combettes, Synthèse ensembliste d'ondelettes, Proceedings of the Conference on Time-Frequency, Wavelets, and Multiresolution, pp. 14.1–14.10. Lyon, France, March 9–11, 1994.

1993

[J10]

P. L. Combettes, Signal recovery by best feasible approximation, IEEE Transactions on Image Processing, vol. 2, no. 2, pp. 269–271, April 1993.

[J09]

P. L. Combettes, The foundations of set theoretic estimation, Proceedings of the IEEE, vol. 81, no. 2, pp. 182–208, February 1993. [pdf]

[C15]

P. L. Combettes and T. J. Chaussalet, Estimation en présence de modèles incertains: Sélection de formulations ensemblistes, Proceedings of the 14th GRETSI Symposium, pp. 205–208. Juan-les-Pins, France, September 13–16, 1993.

[C14]

P. L. Combettes, A simultaneous projection method for inconsistent signal and image feasibility problems, Proceedings of the Eighth IEEE Workshop on Image and Multidimensional Signal Processing, pp. 32–33. Cannes, France, September 8–10, 1993.

[C13]

P. L. Combettes and H. Puh, Parallel projection methods for set theoretic signal reconstruction and restoration, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 297–300. Minneapolis, MN, April 27–30, 1993.

[C12]

P. Bondon, P. L. Combettes, and B. Picinbono, Volterra prediction models and higher order whiteness, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 212–215. Minneapolis, MN, April 27–30, 1993.

1992

[J08]

P. L. Combettes, Convex set theoretic image recovery: History, current status, and new directions, Journal of Visual Communication and Image Representation, vol. 3, no. 4, pp. 307–315, December 1992.

[J07]

P. L. Combettes and H. J. Trussell, Best stable and invertible approximations for ARMA systems, IEEE Transactions on Signal Processing, vol. 40, no. 12, pp. 3066–3069, December 1992.

[J06]

J. W. Silverstein and P. L. Combettes, Signal detection via spectral theory of large dimensional random matrices, IEEE Transactions on Signal Processing, vol. 40, no. 8, pp. 2100–2105, August 1992. [pdf of long version]

[J05]

M. S. Zilovic, L. M. Roytman, P. L. Combettes, and M. N. S. Swamy, A bound for the zeros of polynomials, IEEE Transactions on Circuits and Systems I, vol. 39, no. 6, pp. 476–478, June 1992.

[C11]

J. W. Silverstein and P. L. Combettes, Large dimensional random matrix theory for signal detection and estimation in array processing, Proceedings of the Sixth IEEE Workshop on Statistical Signal and Array Processing, pp. 276–279. Victoria, BC, Canada, October 7–9, 1992.

[C10]

P. L. Combettes and W. W. Edmonson, What is a good estimate?, Proceedings of the European Signal Processing Conference, pp. 713–716. Brussels, Belgium, August 24–27, 1992.

[C09]

P. L. Combettes, M. Benidir, and B. Picinbono, A general framework for the incorporation of uncertainty in set theoretic estimation, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 3, pp. 349–352. San Francisco, CA, March 23–26, 1992.

1991

[J04]

P. L. Combettes and H. J. Trussell, Set theoretic estimation by random search, IEEE Transactions on Signal Processing, vol. 39, no. 7, pp. 1669–1671, July 1991.

[J03]

P. L. Combettes and H. J. Trussell, The use of noise properties in set theoretic estimation, IEEE Transactions on Signal Processing, vol. 39, no. 7, pp. 1630–1641, July 1991. [pdf]

[C08]

P. L. Combettes and T. J. Chaussalet, Critères de qualité en estimation ensembliste, Proceedings of the 13th GRETSI Symposium, pp. 249–252. Juan-les-Pins, France, September 16–20, 1991.

[C07]

P. L. Combettes and M. R. Civanlar, The foundations of set theoretic estimation, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2921–2924. Toronto, Canada, May 14–17, 1991.

1990

[J02]

P. L. Combettes and H. J. Trussell, Method of successive projections for finding a common point of sets in metric spaces, Journal of Optimization Theory and Applications, vol. 67, no. 3, pp. 487–507, December 1990. [pdf]

[C06]

P. L. Combettes and H. J. Trussell, Set theoretic autoregressive spectral estimation, Proceedings of the Fifth IEEE ASSP Workshop on Spectrum Estimation and Modeling, pp. 261–264. Rochester, NY, October 10–12, 1990.

[C05]

P. L. Combettes and H. J. Trussell, New methods for the synthesis of set theoretic estimates, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2531–2534. Albuquerque, NM, April 3–6, 1990.

1989

[J01]

P. L. Combettes and H. J. Trussell, Methods for digital restoration of signals degraded by a stochastic impulse response, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 3, pp. 393–401, March 1989.

[C04]

P. L. Combettes and H. J. Trussell, General order moments in set theoretic estimation, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2531–2534. Glasgow, Scotland, May 23–26, 1989.

1988

[C03]

P. L. Combettes and H. J. Trussell, Stability of the linear prediction filter: A set theoretic approach, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2288–2291. New York, NY, April 11–14, 1988.

1987

[C02]

P. L. Combettes and H. J. Trussell, Modèles et algorithmes en vue de la restauration numérique d'images rayons-X, Proceedings of MARI-Cognitiva Electronic Image, pp. 146–151. Paris, France, May 18–22, 1987. [pdf]

[C01]

H. J. Trussell and P. L. Combettes, Considerations for the restoration of stochastic degradations, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 1209–1212. Dallas, TX, April 6–9, 1987.

Citations

• Most cited mathematician
• MathSciNet
• Publons
• ResearchGate
• Semantic Scholar

Recent conference talks

• Integral proximal mixtures, 4th International Conference on Variational Analysis and Optimization. Santiago, Chile, January 14–17, 2025.

• Randomly activated proximal methods for nonsmooth convex minimization, European Signal Processing Conference. Lyon, France, August 26–30, 2024.

• Signal recovery with proximal comixtures, European Signal Processing Conference. Lyon, France, August 26–30, 2024.

• Proximal expectations, 9th European Congress of Mathematics. Seville, Spain, July 15–19, 2024.

• The geometry of monotone operator splitting, One World Optimization Workshop. Vienna, Austria, June 3–7, 2024.

• Arbitrary products of monotone operators, 3rd International Conference on Variational Analysis and Optimization. Santiago, Chile, January 16–19, 2024.

• Solving monotone inclusions involving nonlinear compositions, 15th International Seminar on Optimization and Related Areas. Arequipa, Peru, October 2–6, 2023.

• A perturbation framework for convex minimization with nonlinear compositions, 10th International Congress on Industrial and Applied Mathematics. Tokyo, Japan, August 20–25, 2023.

• Proximal compositions and cocompositions, Conference on Nonsmooth and Variational Analysis. Dijon, France, June 26–28, 2023.

• A variational inequality model for learning neural networks, IEEE International Conference on Acoustics, Speech, and Signal Processing. Rhodes Island, Greece, June 4–10, 2023.

• Resolvent and proximal compositions, Workshop on Optimization, Learning, and Games. Viña del Mar, Chile, January 8–11, 2023.

• A monotone operator approach to convex Nash equilibria, European Association of Operational Research Societies Conference. Espoo, Finland, July 3–6, 2022.

• Block-activated algorithms for multicomponent fully nonsmooth minimization, IEEE International Conference on Acoustics, Speech, and Signal Processing. Singapore, May 22–27, 2022.

• Signal recovery from inconsistent nonlinear observations, IEEE International Conference on Acoustics, Speech, and Signal Processing. Singapore, May 22–27, 2022.

• Image recovery from perturbed nonlinear observations, SIAM Conference on Imaging Science. Berlin, Germany, March 21–25, 2022.

• Warped resolvent iterations, Workshop on Optimization and Operator Theory dedicated to Professor Lev Bregman. Haifa, Israel, November 15–17, 2021.

• Signal recovery and synthesis from nonlinear equations models, Signal Processing Symposium 2021. Tokyo, Japan, November 9–12, 2021.

• Solving composite fixed point problems with block updates, IFIP Conference on System Modelling and Optimization. Quito, Ecuador, August 30–September 3, 2021.

• Solving composite fixed point problems with block updates, SIAM Conference on Optimization. Spokane, USA, July 20–23, 2021.

• Multivariate monotone inclusions in saddle form, 18th Workshop on Advances in Continuous Optimization (EUROPT). Toulouse, France, July 7–9, 2021.

• Reconstruction of functions from prescribed proximal points, Mathematical Symposium in Memory of Professor Noli Reyes. Quezon City, Philippines, June 5, 2021.

• Proximal analysis of deep neural networks, 2020 Winter Meeting of the Canadian Mathematical Society. Montréal, Canada, December 3–8, 2020.

• Back to single-resolvent iterations, with warping, One World Optimization Seminar. Earth, Universe, May 25, 2020. [slides] [video]

• Variational and proximal analysis of neural networks, Workshop on Optimization and Variational Analysis, in honor of Terry Rockafellar's 85th birthday. Santiago, Chile, January 20–21, 2020.

• The warped proximal point algorithm, International Seminar on Optimization and Related Areas. Lima, Peru, October 7–11, 2019.

• Fully proximal splitting algorithms in image recovery, European Signal Processing Conference. A Coruña, Spain, September 2–6, 2019.

• Bregman-based forward-backward splitting for monotone inclusions, International Conference on Continuous Optimization. Berlin, Germany, August 5–8, 2019.

• The pervasiveness of proximal point iterations – with a proximal analysis of neural networks, Fifth Bay Optimization Meeting. Santa Cruz, CA, May 17, 2019.

• Between subdifferentials and monotone operators, Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions. Vienna, Austria, February 25-March 1, 2019.

• Perspective maximum likelihood-type estimation via proximal decomposition, Mes Temático en Análisis Variacional y Teoría de Juegos. Santiago, Chile, January 9, 2019.

• Purely implicit first order splitting methods, 69th Workshop on Variational Analysis and Applications. Erice, Italy, Aug. 28–Sept. 5, 2018.

• Proximal activation of smooth functions in splitting algorithms for convex minimization, 10th Asian Conference on Fixed Point Theory and Optimization. Chiang Mai, Thailand, July 16–18, 2018.

• Monotone operator theory in convex optimization, International Symposium on Mathematical Programmming. Bordeaux, France, July 1–6, 2018. [slides]

• Proximal activation of smooth functions in splitting algorithms for convex minimization, Workshop Fundamentals and Algorithms for Structured Optimization. Toulouse, France, June 28–29, 2018.

• Image recovery by block-iterative asynchronous proximal splitting," SIAM Conference on Imaging Science. Bologna, Italy, June 5–8, 2018.

• Self-dual classes of operators in nonlinear analysis and optimization, SIAM Great Lakes Section Annual Meeting. Detroit, USA, April 21, 2018.

• Data analysis via perspective functions, Conference on Machine Learning and Optimisation in Economics. London, England, March 8–9, 2018.

• Primal-dual monotone operator splitting by successive outer Bregman projections, International Workshop on Optimization and Variational Analysis. Termas de Cauquenes, Chile, January 10–11, 2018.

• Méthodes d'éclatement d'opérateurs primales-duales monotones au sens de Bregman, Journées Annuelles des GdR MOA et MIA. Bordeaux, France, October 17–20, 2017.

• Parallel, block-iterative, primal-dual monotone operator splitting, BIRS Workshop on Splitting Algorithms, Modern Operator Theory, and Applications. Oaxaca, Mexico, September 17–22, 2017. [video]

• Optimization via nonautonomous difference equations with affine weights, Eighth French-Chilean Optimization Conference. Toulouse, France, July 4–7, 2017.

• Perspective-based proximal data processing, SIAM Conference on Optimization. Vancouver, Canada, May 22–25, 2017.

• Perspective functions: Constructions and applications, Jon Borwein's remembrance conference. Institut Henri Poincaré, Paris, France, February 10, 2017.

• Fonctions perspectives et statistique en grande dimension, 1ère Journée Statistiques-Optimisation MAS-MODE de la SMAI. Paris, France, January 9, 2017.

• Méthodes proximales pour la régression statistique en grande dimension via des fonctions perspectives, Journées Annuelles du GdR MOA. Saint-Anne, Guadeloupe, France, November 20–24, 2016.

• Block-iterative asynchronous variational image recovery, Workshop on Optimization in Image Processing. Harvard University, Cambridge, MA, June 27–30, 2016.

• Méthodes asynchrones d'éclatement d'opérateurs avec balayage par blocs, Conférence SMAI-MODE 2016. Toulouse, France, March 23–25, 2016.

• Asynchronous block-iterative proximal processing of large data sets, International Conference Optimization without Borders, in Honor of Yurii Nesterov's 60th Birthday. Les Houches, France, February 7–12, 2016.

• Horizontal and vertical block decomposition of monotone operator splitting algorithms," International Conference on Variational Analysis, Optimization, and Quantitative Finance in Honor of Terry Rockafellar's 80th Birthday. Limoges, France, May 18–22, 2015.

• Splitting techniques in the face of huge problem sizes: Block-coordinate approaches, Optimization and Big Data 2015. Edinburgh, Scotland, May 6–9, 2015.

• Un processus itératif stochastique et ses applications à l'éclatement d'opérateurs par blocs de variables, Journées annuelles du GdR Mathématiques de l'Optimisation et Applications. Limoges, France, December 3–5, 2014.

• Some aspects of the interplay between convex analysis and monotone operator theory, Worshop on Optimization and Dynamical Processes in Learning and Inverse Problems. Sestri-Levante, Italy, September 8–12, 2014.

• Relaxation of inconsistent common zero problems, Second International Conference on Variational Analysis and Optimization. Santiago, Chile, January 7–10, 2014.

• On the formulation of inverse problems as minimization problems, First Workshop on Optimization for Image and Signal Processing. École Polytechnique, Palaiseau, France, November 18–20, 2013.

• Can one genuinely split m>2 monotone operators? Workshop on Algorithms and Dynamics for Games and Optimization. Playa Blanca, Tongoy, Chile, October 14–18, 2013. [pdf]

• From convex feasibility to optimization in signal recovery and learning, SPARS 2013 - Signal Processing with Adaptive Sparse Structured Representations. Lausanne, Switzerland, July 8–11, 2013.

• Parallel-sum approximation of inconsistent common zero problems, 26th European Conference on Operations Research. Rome, Italy, July 1–4, 2013.

• Systems of structured monotone inclusions: Duality, algorithms, and applications, Nonlinear Optimization: a Bridge from Theory to Applications. Erice, Italy, June 10–17, 2013.

• Algorithmes proximaux pour les problèmes d'optimisation structurés, Horizon Maths Conference. La Défense, France, December 19–20, 2012.

• Moreau's proximal decomposition in Banach spaces, ALEL 2012 Conference on Optimization. Limoges, France, July 2–4, 2012.

• The dynamics of forward-backward splitting, Games and Strategy in Paris. Paris, France, June 11–13, 2012.

• Une extension de la décomposition proximale de Moreau, Journées Annuelles du GdR MOA. Saint-François, Guadeloupe, France, 4–7 juin 2012.

• How many splitting algorithms are there? Latin American Workshop on Optimization and Control. Valparaíso, Chile, January 10–13, 2012.

• Solving composite variational image recovery problems: Recent developments and old myths, Symposium on Variational Image Analysis. Heidelberg, Germany, July 4–7, 2011.

• Monotone+skew decomposition of inclusion problems: algorithms and applications, Computational and Analytical Mathematics. Vancouver, Canada, May 16–20, 2011.

• On the cycles in the method of periodic projections, Escola de Verão em Otimização e Aplicações. Florianópolis, Brazil, March 28-April 1, 2011.

• Open questions around the Baillon-Haddad theorem, French-Chilean Workshop on Dynamics, Optimization and Learning. Valparaíso, Chile, November 22–26, 2010.

• Proximity and information, Riken Conference on Mathematical Sciences and Their Applications. Kamisuwa, Japan, September 19-October 2, 2010.

• Solving composite monotone inclusions, Second South Pacific Conference on Mathematics. Nouméa, Nouvelle-Calédonie, France, August 30-September 3, 2010.

• Splitting methods for constructing the resolvent of a sum of maximal monotone operators, Workshop on Functional Analysis and Optimization. Sevilla, Spain, April 12–13, 2010.

• Méthodes d'éclatement proximales en traitement de l'image, Deuxième Colloque Mathématiques pour l'Image. Orléans, France, March 29-April 1st, 2010.

• Proximal splitting methods in signal recovery, Mathematics and Image Analysis 2009 - MIA'09 . Paris, France, December 14–16, 2009. [slides]

• Duality schemes for solving inclusions, with applications to inverse problems, Interdisciplinary Workshop on Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Banff, Canada, November 1–6, 2009.

• Primal-dual solution of some monotone inclusions, Conference on Variational Analysis and Optimization. Montpellier, France, September 9–12, 2009.

• Fenchel-Rockafellar dualization of signal recovery problems, Approximation and Optimization in Image Restoration and Reconstruction. Porquerolles, France, June 8–12, 2009.

• Proximal methods for nonsmooth inverse problems, International Conference on Scientific Computing and Partial Differential Equations. Hong Kong, December 8–13, 2008.

• Splitting methods for the resolvent of a sum of monotone operators, West Coast Optimization Meeting. Kelowna, Canada, September 5–6, 2008.

• Dykstra's method for monotone operators, Dynamics and Optimization Conference. Paris, France, June 9–11, 2008.

• On the moment problem, Sixth Franco-Chilean Optimization Conference. Toulon, France, May 19–21, 2008.

• Visco-penalization of the sum of two monotone operators, Seventh International Conference on Optimization: Techniques and Applications. Kobe, Japan, December 12–15, 2007.

• Sparsities and iterative thresholding, Rencontre sur le Traitement Mathématique des Images. CIRM, Luminy, France, September 3–7, 2007.

• Cyclic minimizations, Conférence Optimisation, Jeux et Dynamique de la Décision. Avignon, France, June 25–26, 2007.

• Proximal thresholding algorithm for minimization over orthonormal bases, International Conference on Nonlinear and Variational Analysis. Limoges, France, June 20–22, 2007.

• Signal-theoretic applications of monotone operator splitting methods, International Conference on Mathematics of Optimization and Decision Making. Guadeloupe, France, April 18–21, 2006.

• Convergence of approximating curves for monotone inclusions and their associated dynamical systems, International Congress on the Applications of Mathematics. Santiago, Chile, March 13–17, 2006.

• Décomposition d'opérateurs pour les formulations variationnelles lisses et non-lisses en traitement de l'image, Journées Mathématiques de l'Image. Nice, France, January 12–13, 2006.

• Operator splitting methods in inverse problems, First South Pacific Conference on Mathematics. Nouméa, Nouvelle Calédonie, France, August 29-September 2, 2005.

• Viscosity solutions of joint equilibrium problems, VII French-Latin American Congress on Applied Mathematics. Santiago, Chile, January 11–18, 2005.

• Proximal image denoising and recovery, Workshop Contenu Informatif des Images Numériques. Cachan, France, November 25–26, 2004.

Events: conference and seminar organization

• Nonlinear Analysis Seminar (online)
  Department of Mathematics, North Carolina State University [web]

• Neuvièmes Journées Franco-Chiliennes d'Optimisation
  Perpignan, France, 29 juin–1er juillet 2022. [web]

• 3rd Workshop on Operator Splitting Methods in Data Analysis
  Flatiron Institute, New York, USA, March 2020 [web]

• 2nd Workshop on Operator Splitting Methods in Data Analysis
  New York, USA, March 2019 [web]

• 1st Workshop on Operator Splitting Methods in Data Analysis
  SAMSI, Research Triangle Park, USA, March 2018 [web]

• French Days on Optimization & Decision Science
  Autrans, France, March 2018 [web] [poster]

• GdR MOA
  Guadeloupe, France, Novembre 2016 [web]

• Data Science 2015
  Paris, France, Juillet 2015 [web]

• Ottimizzazione e Processi Dinamici in Apprendimento istico e Problemi Inversi
  Sestri Levante, Italia, Settembre 2014 [web]

• Algorithms and Dynamics for Games and Optimization
  Playa Blanca, Chile, October 2013 [web]

• Optimization, Games, and Dynamics
  Paris, France, November 2011 [web]

• Dynamiques, Optimisation et Apprentissage
  Valparaiso, Chile, November 2010 [web]

• Fixed-Point Algorithms for Inverse Problems in Science and Engineering
  Banff, Canada, November 2009 [web]

• Approximation and Optimization in Image Restoration and Reconstruction
  Porquerolles, France, June 2009 [web]

• Conférence sur l'Optimisation and la Décision
  Paris, France, Avril 2007 [web]

• Mathematical Methods for Multi-Channel Image Processing
  Beijing, China, July 2006 [web]

• Mathématiques du Traitement de l'Image
  Hanoi, Vietnam, Septembre 2004 [web]

• Mathématiques de l'Optimisation et de la Décision
  Le Havre, France, Mars 2004 [web]

• Monotone Operators and Applications
  Nice, France, February 2003 [web]

• CEMRACS
  Luminy, France, Juillet 2002 [web]

Teaching

• MA719 Vector Space Methods in Systems Optimization – Optima and Equilibria, Fall 2025 [syllabus]

• MA715 Measure and Integration Theory, Spring 2025 [syllabus]

• MA542 Convex Optimization Methods in Data Science, Spring 2025 [syllabus]

• MA493/MA591 Introduction to Hilbert Spaces, Fall 2024 [syllabus]

• MA532 Dynamical Systems and Ordinary Differential Equations, Spring 2024 [syllabus]

• MA716 Advanced Functional Analysis, Fall 2023 [syllabus]

• MA797 Convex Analysis, Fall 2021 [syllabus]

Academic genealogy

Mathematics Genealogy Project

• Sharaf al-Dīn al-Ṭūsī
• Kamāl al-Dīn Ibn Yūnus
• Nasir al-Dīn al-Ṭūsī
• Shams al‐Dīn al‐Bukhārī (Maragheh Observatory)
• Gregory Chioniadis (Ilkhans Court at Tabriz, 1296)
• Manuel Bryennios
• Theodore Metochites (1315)
• Gregory Palamas
• Nilos Kabasilas (1363)
• Demetrios Kydones
• Georgios Plethon Gemistos (1380)
• Basilios Bessarion (Mystras, 1436)
• Johannes Argyropoulos (Università degli Studi di Padova, 1444)
• Marsilio Ficino (Università degli Studi di Firenze, 1462)
• Angelo Poliziano (Università degli Studi di Firenze, 1477)
• Scipione Fortiguerra (Università degli Studi di Firenze, 1493)
• Girolamo Aleandro (Università degli Studi di Padova, 1499)
• Rutger Rescius (Université de Paris, 1513)
• Johannes Winter von Andernach (Université de Louvain, 1527)
• Guillaume Rondelet (Université de Paris, 1538)
• Felix Plater (Université de Montpellier, 1557)
• Petrus Ryff (Universität Basel, 1584)
• Emmanuel Stupanus (Universität Basel, 1613)
• Nikolaus Eglinger (Universität Basel, 1660)
• Johann Bernoulli (Universität Basel, 1690)
• Leonhard Euler (Universität Basel, 1726)
• Joseph-Louis Lagrange (Università di Torino, 1754)
• Siméon D. Poisson (École Polytechnique, 1800)
• Michel Chasles (École Polytechnique, 1814)
• Hubert A. Newton (Yale University, 1850)
• E. Hastings Moore (Yale University, 1885)
• George D. Birkhoff (University of Chicago, 1907)
• Marshall H. Stone (Harvard University, 1926)
• William F. Eberlein (Harvard University, 1942)
• A. Wayne Wymore (University of Wisconsin-Madison, 1955)
• Bobby R. Hunt (University of Arizona, 1967)
• H. Joel Trussell (University of New Mexico, 1976)
• Patrick L. Combettes (North Carolina State University, 1989)
• Hong Puh (City University of New York, 1996)
• Jian Luo (City University of New York, 2000)
• Sever A. Hirstoaga (Université Pierre et Marie Curie, 2006)
• Valérie R. Wajs (Université Pierre et Marie Curie, 2007)
• Thomas D. Capricelli (Université Pierre et Marie Curie, 2008)
• Luis M. Briceño-Arias (Université Pierre et Marie Curie, 2011)
• Bằng Công Vũ (Université Pierre et Marie Curie, 2013)
• Quang Văn Nguyễn (Université Pierre et Marie Curie, 2015)
• Lilian E. Glaudin (Sorbonne Université, 2019)
• Zev C. Woodstock (North Carolina State University, 2021)
• Minh N. Bùi (North Carolina State University, 2021)

People

Current Ph.D. students

• Diego J. Cornejo
• Javier I. Madariaga
• Julien N. Mayrand

Former Ph.D. students

• Minh N. Bùi, North Carolina State University, 2021
  The Warped Resolvent of a Set-Valued Operator: Theory and Applications

• Zev C. Woodstock, North Carolina State University, 2021
  Construction of Functions from Nonlinear Transformations

• Lilian E. Glaudin, Sorbonne Université (formerly Université Pierre et Marie Curie), 2019
  Stratégies Multicouche, avec Mémoire, et à Métrique Variable en Méthodes de Point Fixe pour l'Éclatement d'Opérateurs Monotones et l'Optimisation
  (Strategies with Multiple Layers, Memory, and Variable Metric in Fixed Point Methods for Monotone Operator Splitting and Optimization)

• Quang Văn Nguyễn, Université Pierre et Marie Curie, 2015
  Méthodes d'Éclatement Basées sur les Distances de Bregman pour les Inclusions Monotones Composites et l'Optimisation
  (Splitting Methods Based on Bregman Distances for Composite Monotone Inclusions and Optimization)

• Bằng Công Vũ, Université Pierre et Marie Curie, 2013
  Inclusions Monotones en Dualité et Applications
  (Monotone Inclusions in Duality and Applications)

• Luis M. Briceño-Arias, Université Pierre et Marie Curie, 2011
  Problèmes d'Inclusions Couplées : Éclatement, Algorithmes et Applications
  (Coupled Inclusions Problems: Splitting, Algorithms, and Applications)

• Thomas D. Capricelli, Université Pierre et Marie Curie, 2008
  Algorithmes de Projections Convexes Généralisées et Applications en Imagerie Médicale
  (Generalized Convex Projection Algorithms and Applications in Medical Imaging)

• Valérie R. Wajs, Université Pierre et Marie Curie, 2007
  Décompositions et Algorithmes Proximaux pour l'Analyse et le Traitement Itératif des Signaux
  (Proximal Decompositions and Algorithms for Signal Analysis and Iterative Signal Processing)

• Sever A. Hirstoaga, Université Pierre et Marie Curie, 2006
  Approximation et Résolution de Problèmes d'Équilibre, de Point Fixe et d'Inclusion Monotone
  (Approximation and Numerical Solution of Equilibrium, Fixed Point, and Monotone Inclusion Problems)

• Jian Luo, City University of New York, 2000
  Non-Differentiable Constrained Signal Restoration by Subgradient Level Methods

• Hong Puh, City University of New York, 1996
  Operator Theoretic Image Coding

Nonlinear Analysis Thematic Group

[web]