2002

Attouch, Hédy, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Redont, Patrick (2002) Optimizing Properties of an Inertial Dynamical System with Geometric Damping. Link with Proximal Methods. Control and Cybernetics, 31 (3). pp. 643-657.

Alvarez, Felipe, Attouch, Hédy, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Redont, Patrick (2002) A Second-Order Gradient-Like Dissipative Dynamical System with Hessian-Driven Damping. Application to Optimization and Mechanics. Journal de Mathématiques Pures et Appliquées, 81 (8). pp. 747-779.

2003

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 (2003) Continuous Gradient Projection Method in Hilbert Spaces. Journal of Optimization Theory and Applications, 119 (2). pp. 235-259.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Teboulle, Marc (2003) Barrier Operators and Associated Gradient-Like Dynamical Systems for Constrained Minimization Problems. SIAM Journal on Control and Optimization, 42 (4). pp. 1266-1292.

2004

Alvarez, Felipe, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Brahic, Olivier (2004) Hessian Riemannian Gradient Flows in Convex Programming. SIAM Journal on Control and Optimization, 43 (2). pp. 477-501.

Attouch, Hédy, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Redont, Patrick and Teboulle, Marc (2004) A Singular Riemannian Barrier Method for Constrained Minimization. Optimization, 53 (5-6). pp. 435-454.

2005

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris, Lewis, Adrian and Shiota, Masahiro (2005) Clarke Critical Values of Subanalytic Lipschitz Continuous Functions. Annales Polonici Mathematici, 87. pp. 13-25.

2006

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris and Lewis, Adrian (2006) A Nonsmooth Morse-Sard Theorem for Subanalytic Functions. Journal of Mathematical Analysis and Applications, 321 (2). pp. 729-740.

2007

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris, Lewis, Adrian and Shiota, Masahiro (2007) Clarke Subgradients of Stratifiable Functions. SIAM Journal on Optimization, 18 (2). pp. 556-572.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris and Lewis, Adrian (2007) The Lojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems. SIAM Journal on Optimization, 17 (4). pp. 1205-1223.

2008

Attouch, Hédy, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Redont, Patrick and Soubeyran, Antoine (2008) Alternating Proximal Algorithms for Weakly Coupled Minimization Problems. Applications to Dynamical Games and PDE’s. Journal of Convex Analysis, 15 (3). pp. 485-506.

Alvarez, Felipe, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Munier, J. (2008) A Unifying Local Convergence Result for Newton's Method in Riemannian Manifolds. Foundations of Computational Mathematics, 8 (2). pp. 197-226.

2009

Attouch, Hédy and Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 (2009) On the Convergence of the Proximal Algorithm for Nonsmooth Functions Involving Analytic Features. Mathematical Programming, 116 (1-2). pp. 5-16.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris and Lewis, Adrian (2009) Tame Functions are Semismooth. Mathematical Programming, 117 (1-2). pp. 5-19.

2010

Attouch, Hédy, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Redont, Patrick and Soubeyran, Antoine (2010) Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality. Mathematics of Operations Research, 35 (2). pp. 438-457.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris, Ley, Olivier and Mazet, Laurent (2010) Characterizations of Lojasiewicz Inequalities and Applications. Transactions of the American Mathematical Society, 362 (6). pp. 3319-3363.

2011

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Daniilidis, Aris and Lewis, Adrian (2011) Generic Optimality Conditions for Semialgebraic Convex Programs. Mathematics of Operations Research, 36 (1). pp. 55-70.

2012

Alvarez, Felipe, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Bonnans, Frédéric and Silva-Àlvarez, Francisco José (2012) Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems. Mathematical Programming, 135 (n°1-2). pp. 473-507.

2013

Attouch, Hédy, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Svaiter, Benar Fux (2013) Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel method. Mathematical Programming, 137 (1-2). pp. 91-129.

2014

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Sabach, Shoham and Teboulle, Marc (2014) Proximal alternating linearized method for nonconvex and nonsmooth problems. Mathematical Programming, 146. pp. 459-494.

2015

Bobtcheff, Catherine, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Mariotti, ThomasORCID: https://orcid.org/0000-0002-0525-8743 (2015) Researcher's Dilemma. TSE Working Paper, n. 13-377, Toulouse

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Gaubert, Stéphane and Vigeral, Guillaume (2015) Definable zero-sum stochastic games, Mathematics of Operations Research. Mathematics of Operations Research, vol.40 (n°1). pp. 171-191.

Bégout, PascalORCID: https://orcid.org/0000-0002-9172-3057, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Jendoubi, Mohamed Ali (2015) On damped second-order gradient systems. Journal of Differential Equations, 259 (7). pp. 3115-3143.

Bégout, PascalORCID: https://orcid.org/0000-0002-9172-3057, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Jendoubi, Mohamed Ali (2015) On damped second-order gradient systems. Journal of Differential Equations, vol. 259 (n° 7-8). pp. 3115-3143.

2016

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Pauwels, Edouard (2016) Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs. Mathematics of Operations Research, vol. 41 (n° 2). pp. 442-465.

Bauschke, H. H., Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Teboulle, Marc (2016) A descent Lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications. Mathematics of Operations Research, 42 (n°2). pp. 330-348.

2017

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Nguyen, Trong Phong, Peypouquet, Juan and Suter, Bruce W. (2017) From error bounds to the complexity of first-order descent methods for convex functions. Mathematical Programming, 165 (2). pp. 471-507.

Bauschke, H. H., Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Teboulle, Marc (2017) A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications. Mathematics of Operations Research, 42 (2). pp. 330-348.

Blanchet, Adrien and Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 (2017) A family of functional inequalities: lojasiewicz inequalities and displacement convex functions. TSE Working Paper, n. 17-787, Toulouse

Bobtcheff, Catherine, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Mariotti, ThomasORCID: https://orcid.org/0000-0002-0525-8743 (2017) Researcher's Dilemma -. Review of Economic Studies, 84 (3). pp. 969-1014.

2018

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Sabach, Shoham and Teboulle, Marc (2018) Nonconvex Lagrangian-based optimization: Monitoring schemes and global convergence. Mathematics of Operations Research, vol. 43 (n° 4). pp. 1051-1404.

Blanchet, Adrien and Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 (2018) A family of functional inequalities: Lojasiewicz inequalities and displacement convex functions. Journal of Functional Analysis, vol. 275 (n° 7). pp. 1650-1673.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Sabach, Shoham, Teboulle, Marc and Vaisbourd, Y. (2018) First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems. SIAM Journal on Optimization, 28 (3). pp. 2131-2151.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Hochart, Antoine and Pauwels, Edouard (2018) Qualification conditions in semi-algebraic programming. SIAM Journal on Optimization, 28 (2). pp. 1867-1891.

2019

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Pauwels, Edouard (2019) Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning. Mathematical Programming. pp. 1-33. (In Press)

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Castera, Camille, Pauwels, Edouard and Févotte, Cédric (2019) An Inertial Newton Algorithm for Deep Learning. TSE Working Paper, n. 19-1043, Toulouse

2020

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Chen, Zheng and Pauwels, Edouard (2020) The multiproximal linearization method for convex composite problems. Mathematical Programming, vol. 182. pp. 1-36.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Pauwels, Edouard and Rios-Zertuche, Rodolfo (2020) Long term dynamics of the subgradient method for Lipschitz path differentiable functions. TSE Working Paper, n. 20-1110, Toulouse

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Pauwels, Edouard (2020) Curiosities and counterexamples in smooth convex optimization. TSE Working Paper, n. 20-1080, Toulouse

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407 and Pauwels, Edouard (2020) A mathematical model for automatic differentiation in machine learning. In: Advances in Neural Information Processing Systems 33 (NeurIPS 2020) Larochelle, Hugo, Ranzato, M., Hadsell, R., Balcan, M.F. and Lin, H. (eds.) MIT Press. ISBN 9781713829546 (In Press)

2021

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Glaudin, Lilian, Pauwels, Edouard and Serrurier, Matthieu (2021) A Hölderian backtracking method for min-max and min-min problems. TSE Working Paper, n. 21-1243, Toulouse

Bolte, Jérôme, Le, Tam, Pauwels, Edouard and Silveti Falls, AntonioORCID: https://orcid.org/0000-0002-8165-6348 (2021) Nonsmooth implicit differentiation for machine learning and optimization. In: NIPS'21: 35th International Conference on Neural Information Processing Systems, 6-14 décembre 2021, En ligne.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Bertoin, David, Gerchinovitz, Sébastien and Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X (2021) Numerical influence of ReLU’(0) on backpropagation. Advances in Neural Information Processing Systems, Vol. 34. pp. 468-479.

2022

Dragomir, Radu, Taylor, Adrien B., Bolte, Jérôme and D'Aspremont, Alexandre (2022) Optimal complexity and certification of Bregman first-order methods. Mathematical Programming, 194. pp. 41-83.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Combettes, Cyrille and Pauwels, Edouard (2022) The Iterates of the Frank-Wolfe Algorithm May Not Converge. TSE Working Paper, n. 22-1311, Toulouse

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Le, Tam and Pauwels, Edouard (2022) Subgradient sampling for nonsmooth nonconvex minimization. TSE Working Paper, n. 22-1310, Toulouse

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X and Vaiter, SamuelORCID: https://orcid.org/0000-0002-4077-708X (2022) Automatic differentiation of nonsmooth iterative algorithms. In: 35th conference on neural information processing systems (NeurIPS 2021) Oh, A., Koyejo, S., Mohamed, S., Agarwal, A., Belgrave, D. and Cho, K. (eds.) NeurIPS/Curran Associates. Series “Advances in neural information processing systems, vol.35”, Vol. vol.36. San Mateo pp. 77089-77103. ISBN 9781713871088

2023

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X and Vaiter, Samuel (2023) One-step differentiation of iterative algorithms. Advances in Neural Information Processing Systems 36. pp. 77089-77103.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Glaudin, Lilian, Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X and Serrurier, Matthieu (2023) The backtrack Hölder gradient method with application to min-max and min-min problems. Open Journal of Mathematical Optimization, vol.4 (n°8).

2024

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Combettes, Cyrille and Pauwels, Edouard (2024) The iterates of the Frank–Wolfe algorithm may not converge. Mathematics of Operations Research, Vol. 49 (N° 4). pp. 2049-2802.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Miclo, LaurentORCID: https://orcid.org/0000-0001-5502-2862 and Villeneuve, StéphaneORCID: https://orcid.org/0000-0003-3213-1905 (2024) Swarm gradient dynamics for global optimization: the mean-field limit case. Mathematical Programming, Vol. 205. pp. 661-701.

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X and Silveti Falls, AntonioORCID: https://orcid.org/0000-0002-8165-6348 (2024) Differentiating nonsmooth solutions to parametric monotone inclusion problems. SIAM Journal on Optimization, Vol. 34 (N° 1). pp. 71-97.

2025

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Le, Tam, Moulines, Éric and Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X (2025) Inexact subgradient methods for semialgebraic functions. Mathematical Programming. (In Press)

Bachoc, François, Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Boustany, Ryan and Loubès, Jean-Michel (2025) When majority rules, minority loses: bias amplification of gradient descent. TSE Working Paper, n. 25-1641, Toulouse

2026

Bolte, JérômeORCID: https://orcid.org/0000-0002-1676-8407, Pauwels, EdouardORCID: https://orcid.org/0000-0002-8180-075X, Le, Quoc Tung and Vaiter, Samuel (2026) Geometric and computational hardness of bilevel programming. Mathematical Programming, vol.215. pp. 539-574.