Jean Charles GILBERT

• Emeritus Senior Researcher
  Serena research team
  INRIA (Inria center of Paris)
  48, rue Barrault
  CS 61534
  75647 PARIS Cedex
  France
  
  Telephone: +33 1 80 49 41 20
  E-mail: Jean-Charles.Gilbert@inria.fr
  

• Associate professor
  Mathematics Department (see also the research team Bisous)
  University of Sherbrooke (Québec), Canada.
  

• Identifiers: IdhaL (jean-charles-gilbert), IdRef (070361657), MathSciNet (73490), ORCID (0000-0002-0375-4663)
  Networks: LinkedIn, Viadeo
  Publications: on HAL
  

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
• Complementarity problems
  • Linearization methods for linear and nonlinear complementarity problems
• Touched domains
  • Complex linear algebra
  • Discrete geometry: hyperplane arrangements
  • Matroid
  • Nonsmooth analysis
  • Partial differential equations
• 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
  • 1989-2021: École Nationale Supérieure de Techniques Avancées (ENSTA), 2nd year, Differentiable Optimization - Theory and Algorithms (lecture I and lecture II).
  • 2015-2021: Institut Polytechnique de Paris, M2 Optimization, Advanced Continuous Optimization (description of the course).

Publications

By type

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• Unpublished reports

• All of them
• Optimization
• Complementarity
• Nonsmooth Analysis
• 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, 23rd of April 2015.
• Polyhedral Newton-min algorithms for complementarity problems, Mokaplan Seminar, Inria, Paris, France, 7th of June 2023.

• 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 (1937-2022), Clovis Gonzaga (1944-2021), 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, href="https://www.linkedin.com/in/baptiste-plaquevent-jourdain-1766a2161/?originalSubdomain=fr">Baptiste Plaquevent-Jourdain, 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 (qpalm_0_4.zip, this code was uploaded on 12-06-2023, much after its conception in 2014; in case of difficulty, contact the author), 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 (version 0.4.5), 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).
• Hnm4lcp (version 1.0): Matlab code that solves a linear complementarity problem with a nondegenerate matrix.
• Other pieces of software
  • pgr (Matlab): polyhedral gauge recovery problem solver (minimization of a polyhedral gauge on an affine subspace, with uniqueness detection).
  • nmhp (Matlab): linear complementarity problem solver by the Newton-min algorithm with the Harker and Pang globalization technique.
  • isf-bdiffmin (Matlab, with Jean-Pierre Dussault and Baptiste Plaquevent-Jourdain): bdiffmin computes the B-differential of the componentwise minimum of two affine vector functions. To achieve this task, bdiffmin uses the Matlab function isf, which determines the chambers of an arrangement of hyperplanes having a point in common.

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), Baptiste Plaquevent-Jourdain (2021, April 19 to Septembre 17), Philippe Ségalat (1998), Jan Stuchlý (2006), ...

• Former engineers

• Baptiste Plaquevent-Jourdain (from January 2021, co-directed by Jean-Pierre Dussault University of Sherbrooke, Canada): Robust methods for solving complementarity problems, with extension to structured nonsmooth systems. Mitacs-Globalink scholarship for living expenses in Canada in 2023. The PhD thesis has been submitted on the 3rd of April 2025.

  Publications linked to the PhD thesis

  • On the B-differential of the componentwise minimum of two affine vector functions [view-only] [hal-04048393], J.-P. Dussault, J.Ch.G., B. Plaquevent-Jourdain, Mathematical Programming Computation (to appear).
    On the B-differential of the componentwise minimum of two affine vector functions - The full report, J.-P. Dussault, J.Ch.G., B. Plaquevent-Jourdain, report uploaded on HAL on the 27th of March 2023.
    ISF and BDIFFMIN - Matlab functions for the hyperplane arrangement and the computation of the B-differential of the componentwise minimum of two affine vector functions, J.-P. Dussault, J.Ch.G., B. Plaquevent-Jourdain, report uploaded on HAL on the 23th of May 2023.
  • Primal and dual approaches for the chamber enumeration of real hyperplane arrangements, J.-P. Dussault, J.Ch.G., B. Plaquevent-Jourdain, SIAM Journal on Discrete Mathematics (submitted on March 23, 2025).
    Primal and dual approaches for the chamber enumeration of real hyperplane arrangements - The full report, J.-P. Dussault, J.Ch.G., B. Plaquevent-Jourdain,
  
  
• 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; 2019, 3 months, 2023, 5 weeks; 2024: 2 weeks in March).

Scientific community animation

• Associate editor: SIAM Journal on Optimization (????-????), De Gruyter Book Series on Optimization (2014-2019).
• 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), ...