Article

Bolte, Jérôme, 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, Jérôme, Miclo, Laurent and Villeneuve, Stéphane (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.

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

Bolte, Jérôme, Chen, Zheng and Pauwels, Edouard (2020) The multiproximal linearization method for convex composite problems. Mathematical Programming, vol. 182. pp. 1-36.

Bolte, Jérôme and Pauwels, Edouard (2019) Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning. Mathematical Programming. pp. 1-33. (In Press)

Bolte, Jérôme, 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, Jérôme (2018) A family of functional inequalities: Lojasiewicz inequalities and displacement convex functions. Journal of Functional Analysis, vol. 275 (n° 7). pp. 1650-1673.

Bolte, Jérôme, 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, Jérôme, Hochart, Antoine and Pauwels, Edouard (2018) Qualification conditions in semi-algebraic programming. SIAM Journal on Optimization, 28 (2). pp. 1867-1891.

Bolte, Jérôme, 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, Jérôme 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.

Bobtcheff, Catherine, Bolte, Jérôme and Mariotti, Thomas (2017) Researcher's Dilemma -. Review of Economic Studies, 84 (3). pp. 969-1014.

Bolte, Jérôme 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, Jérôme 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.

Bolte, Jérôme, 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, Pascal, Bolte, Jérôme and Jendoubi, Mohamed Ali (2015) On damped second-order gradient systems. Journal of Differential Equations, 259 (7). pp. 3115-3143.

Bolte, Jérôme, Sabach, Shoham and Teboulle, Marc (2014) Proximal alternating linearized method for nonconvex and nonsmooth problems. Mathematical Programming, 146. pp. 459-494.

Attouch, Hédy, Bolte, Jérôme 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.

Alvarez, Felipe, Bolte, Jérôme, 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.

Bolte, Jérôme, Daniilidis, Aris and Lewis, Adrian (2011) Generic Optimality Conditions for Semialgebraic Convex Programs. Mathematics of Operations Research, 36 (1). pp. 55-70.

Attouch, Hédy, Bolte, Jérôme, 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, Jérôme, 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.

Attouch, Hédy and Bolte, Jérôme (2009) On the Convergence of the Proximal Algorithm for Nonsmooth Functions Involving Analytic Features. Mathematical Programming, 116 (1-2). pp. 5-16.

Bolte, Jérôme, Daniilidis, Aris and Lewis, Adrian (2009) Tame Functions are Semismooth. Mathematical Programming, 117 (1-2). pp. 5-19.

Attouch, Hédy, Bolte, Jérôme, 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, Jérôme 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.

Bolte, Jérôme, Daniilidis, Aris, Lewis, Adrian and Shiota, Masahiro (2007) Clarke Subgradients of Stratifiable Functions. SIAM Journal on Optimization, 18 (2). pp. 556-572.

Bolte, Jérôme, 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.

Bolte, Jérôme, 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.

Bolte, Jérôme, Daniilidis, Aris, Lewis, Adrian and Shiota, Masahiro (2005) Clarke Critical Values of Subanalytic Lipschitz Continuous Functions. Annales Polonici Mathematici, 87. pp. 13-25.

Alvarez, Felipe, Bolte, Jérôme 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, Jérôme, Redont, Patrick and Teboulle, Marc (2004) A Singular Riemannian Barrier Method for Constrained Minimization. Optimization, 53 (5-6). pp. 435-454.

Bolte, Jérôme (2003) Continuous Gradient Projection Method in Hilbert Spaces. Journal of Optimization Theory and Applications, 119 (2). pp. 235-259.

Bolte, Jérôme 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.

Attouch, Hédy, Bolte, Jérôme 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, Jérôme 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.

Book Section

Bolte, Jérôme 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)

Monograph

Bachoc, François, Bolte, Jérôme, Boustany, Ryan and Loubès, Jean-Michel (2025) When majority rules, minority loses: bias amplification of gradient descent. TSE Working Paper, n. 25-1641, Toulouse

Bolte, Jérôme, Le, Tam and Pauwels, Edouard (2022) Subgradient sampling for nonsmooth nonconvex minimization. TSE Working Paper, n. 22-1310, Toulouse

Bolte, Jérôme, 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, 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, Jérôme and Pauwels, Edouard (2020) Curiosities and counterexamples in smooth convex optimization. TSE Working Paper, n. 20-1080, Toulouse

Bolte, Jérôme, Castera, Camille, Pauwels, Edouard and Févotte, Cédric (2019) An Inertial Newton Algorithm for Deep Learning. TSE Working Paper, n. 19-1043, Toulouse

Blanchet, Adrien and Bolte, Jérôme (2017) A family of functional inequalities: lojasiewicz inequalities and displacement convex functions. TSE Working Paper, n. 17-787, Toulouse

Conference or Workshop Item

Bolte, Jérôme, Le, Tam, Pauwels, Edouard and Silveti-Falls, Antonio (2022) 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.