Jean Charles GILBERT

INRIA (research center of Paris)
2, rue Simone Iff
CS 42112
75589 Paris Cedex 12
France

Telephone: +33 1 80 49 41 20
E-mail: Jean-Charles.Gilbert@inria.fr
Identifiers: IdHAL (jean-charles-gilbert), MathSciNet (73490), ORCID (0000-0002-0375-4663)
Networks: LinkedIn, Viadeo

Version française

Interests

Current and previous activities

• Numerical optimization
  • Newton and quasi-Newton methods (smooth and nonsmooth)
  • Augmented Lagrangian approaches in quadratic optimization
  • Interior-point methods in convex optimization, nonlinear optimization, and semidefinite optimisation
  • Sequential quadratic programming (a Newton method in nonlinear optimization)
  • Algebraic methods in derivative-free optimization
  • Decomposition-coordination algorithms for large-scale problems, including in stochastic optimization
  • Stochastic optimisation: scenario decomposition
  • Positive semi-definie optimization: SDP relaxation of algebraic problems
  • Polynomial optimisation: moment-sos method
  • Convex optimization: convex quadratic optimization, L1 and gauge recovery
• Numerical methods for complementarity problems
  • Linearization methods for linear and nonlinear complementarity problems
• Software development
  • See below
• Applications
  • Former applications
  • 2013-2016: Global optimization of the power flow in an electricity transportation network, with Cédric Josz (RTE, Inria, Paris VI), Jean Maeght (RTE), and Patrick Panciatici (RTE).
• Teaching
  • Former teaching
  • 1989-2020: École Nationale Supérieure de Techniques Avancées (ENSTA), 2nd year, Differentiable Optimization - Theory and Algorithms (lecture I and lecture II).
  • 2015-2020: University Paris-Saclay, M2 Optimization, Advanced Continuous Optimization (description of the course).

Publications

• Polyhedral Newton-min algorithms for complementarity problems, with J.-P. Dussault, M. Frappier. Journal of Nonsmooth Analysis and Optimization (submitted), 2019.
• A trust region method based on interior point techniques for nonlinear programming, with R.H. Byrd, and J. Nocedal. Mathematical Programming, 89 (2000) 149-185.
• Global convergence properties of conjugate gradient methods for optimization, with J. Nocedal. SIAM Journal on Optimization, 2 (1992) 21-42.

By type

• All of them
• Books
• Journals, book chapters
• Proceedings
• Lecture notes
• Unpublished reports

• All of them
• Optimization
• Complementarity
• Automatic Differentiation
• Partial differential equations
• Linear algebra
• Applications
• Software

• How the augmented Lagrangian algorithm can deal with an infeasible convex quadratic optimization problem - Motivation, analysis, implementation, séminaire de l'équipe EDP Analyse Numérique, laboratoire J.A. Dieudonné, Nice, France, April 23, 2015.

• Paul Armand, Ibtihel Ben Gharbia, Jacques Blum, Frédéric Bonnans, Richard Byrd, Laurent Chauvier, Alice Chiche, Gilbert Damy, Frédéric Delbos, Jean-Pierre Dussault, Carole Duval, Patrick Erhard, Frédéric Eyssette, Serge Fantino, Christèle Faure, Mathieu Frappier, Antonio Fuduli, J. Gabarro-Arpa, Roland Glowinski, Clovis Gonzaga, Sophie Jan-Jégou, Patrick Joly, Xavier Jonsson, Cédric Josz, Elisabeth Karas, Marc Le Bret, J. Le Foll, Claude Lemaréchal, Georges Le Vey, Jean Maeght, John Masse, Jorge Nocedal, Patrick Panciatici, Nicolas Pichon, Nicole Rostaing, Claudia Sagastizábal, Delphine Sinoquet, Bernard Thooris.

• Erdös number 4
  (Patrick Joly, Gary C. Cohen, Peter Frankl)
  (Roland Glowinski, Wayne M. Lawton, Andrzej Schinzel)

Lecture notes (some in French)

• Algèbre Linéaire (Feuilles de résultats). Pôle Universitaire Léonard de Vinci, Paris.
• Fragments d'Optimisation Différentiable - Théorie et Algorithmes. École Nationale Supérieure de Techniques Avancées (ENSTA), Paris.
• Analyse Fonctionnelle (Feuilles de résultats). Université Paris I (Panthéon-Sorbonne), M2 ``Modélisation et Méthodes Mathématiques en Economie et en Finance''.
• Introduction aux Algorithmes de Points Intérieurs, M2 - OJME. Université de Paris VI.
• Méthodes newtoniennes en optimisation non linéaire, M2 - MMMEF. Université de Paris I.
• Advanced Continuous Optimization, M2 - Optimization, Université Paris-Saclay.
• Step by step design of an interior point solver in semidefinite optimization, M2 - Optimization, Université Paris-Saclay.
• Contributions à la Wikipédia francophone

Software development

• Libopt: an environment for testing solvers on heterogeneous collections of problems (with X. Jonsson).
• M1CG1: implements a CG algorithm for solving in sequence large scale linear systems with similar positive definite matrices; the solver generates an l-BFGS preconditioning matrix that can be used to accelarate finding the solution of the next linear system.
• M1QN3: large-scale unconstrained optimization by a limited memory BFGS method (with C. Lemaréchal).
• Qpalm, Oqla (with Émilie Joannopoulos): two solvers of convex quadratic optimization problems, with the following features:
  • written in Matlab (Qpalm) and C++ (Oqla),
  • augmented Lagrangian method, with minimization of the augmented Lagrangian by an active set method,
  • can deal with an infeasible problem, in which case a solution to the closest feasible problem is computed,
  • can deal with an unbounded problem, in which case an unboundedness direction is computed,
  • the speed of convergence prescribed by the user is ensured (provided rounding error does not prevail),
  • adaptation to an SQP solver of nonlinear optimizatin problems.
• SQPlab, SQPlight et SQPpro: a suite of optimization solvers based on the SQP Newtonian approach.
• Sdolab (version 0.4): Matlab code that solves a semidefinite optimization problem in complex numbers (dense linear algebra).
• Small pieces of software
  • pgr (Matlab): polyhedral gauge recovery problem solver (minimization of a polyhedral gauge on an affine subspace, with uniqueness detection).
  • nmhp 1.1 (Matlab): linear complementarity problem solver by the Newton-min algorithm with the Harker and Pang globalization technique.

Management

• François Akoa (2000), Jean André, Ibtihel Ben Gharbia, Laurent Chauvier (1995), Alice Chiche, Juan Pablo Contreras (2018, April 1 to August 31), Francois Courty, G. Do (1995), Mathieu Frappier (2017), bourse Mitacs-Globalink from Canada, Xavier Jonsson (1997), Souaid Mezouar (2006), Houssem Miled (2005), Philippe Ségalat (1998), Jan Stuchlý (2006), ...

• Former engineers

• Former PhD students
• Mathematics Genealogy Project

• Former post-docs

Visitors

• Jorge Nocedal (around 1992-1995), Richard Byrd (around 1995), Paul Armand (around 2000), Clovis Gonzaga (around 2000), Jean-Pierre Dussault (2017, 1 month).

Scientific community animation

• Associate editor: SIAM Journal on Optimization (????-????), De Gruyter Book Series on Optimization (2014-).
• Member of the selection comity of post-doctoral students: Inria Paris-Rocquencourt (????-2011).
• Member of the selection comities of maîtres de conférence: University of Limoges (????), Enseeiht in Toulouse (2013), University Joseph Fourier, Grenoble I (2013).
• Member of the scientific committee of the conference ISMP 2018 in Bordeaux, France.
• PhD thesis examining committee: Philippe Al Khoury (2005, Paris-Dauphine, reporter), Ibtihel Ben Gharbia (2012, Paris-Dauphine, director), Laurent Chauvier (2000, Paris I Sorbonne, director), Alice Chiche (2012, Paris VI, director), Frédéric Delbos (2004, Paris VI, director), Gabriela Dobranszky (2005, Nice-Sophia Antipolis), Marc Honnorat (2007, Grenoble, reporter), Sophie Jan-Jégou (1997, Paris-Dauphine), M. Joannides (1997, Marseille), Xavier Jonsson (2002, Paris VI, director), Cédric Josz (2016, Paris VI, director), Elisabeth Karas (2002, Paris I Sorbonne, director), Tangi Migot (2017, Rennes, president), Adam Ouorou (2014, HDR, Paris I Sorbonne), Anke Tröltzsch (2011, Toulouse, reporter), D. Villard (1995, Rennes), ...