Jean Charles GILBERT

• Senior Researcher
  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
  

• 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

• On the B-differential of the componentwise minimum of two affine vector functions - The full report, with J.-P. Dussault and B. Plaquevent-Jourdain. Report uploaded on HAL on the 25th of November 2022, submitted to Mathematical Programming Computation (in revision).
• A trust region method based on interior point techniques for nonlinear programming (cited 119/1855 times according to MathSciNet/Google Scholar), with R.H. Byrd, and J. Nocedal. Mathematical Programming, 89 (2000) 149-185.
• Global convergence properties of conjugate gradient methods for optimization (cited 293/1385 times according to MathSciNet/Google Scholar), 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
• 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, 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).
• 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 2022, 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.

  Publication linked to the PhD thesis

  • On 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 27th of March 2023, submitted to Mathematical Programming Computation (in révision).
    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.
  
  
• 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).

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), ...