2002

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.

2003

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.

2004

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.

2005

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.

2006

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.

2007

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.

2008

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.

2009

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.

2010

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.

2011

Bolte, Jérôme, 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, 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.

2013

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.

2014

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

2015

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.

2016

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.

2017

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.

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

Blanchet, Adrien and Bolte, Jérôme (2017) A family of functional inequalities: lojasiewicz inequalities and displacement convex functions. IAST Working Paper, n. 17-66, Toulouse

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

2018

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. 25 (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.

2019

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

2020

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, 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 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, 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

2022

Bolte, Jérôme, Le, Tam, Pauwels, Edouard and Silveti-Falls, Antonio (2022) Nonsmooth Implicit Differentiation for Machine Learning and Optimization. TSE Working Paper, n. 22-1314, Toulouse, France

Bolte, Jérôme, Combettes, Cyrille and Pauwels, Edouard (2022) The Iterates of the Frank-Wolfe Algorithm May Not Converge. TSE Working Paper, n. 22-1311, Toulouse

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

2024

Bolte, Jérôme, Miclo, Laurent and Villeneuve, Stéphane (2024) Swarm gradient dynamics for global optimization: the mean-field limit case. Mathematical Programming. (In Press)