# Lemaréchal

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## Claude Lemaréchal

Claude Lemaréchal was born in Paris in 1944. He graduated at ENSEIHT, one of the prestigious French engineering schools in Toulouse, obtained his "Doctorat d'Etat" (equivalent of today's Habilitation) in mathematics at the University of Paris-Dauphine, and spent most of his career at INRIA a reknowned French research centre for applied mathematics and computer science. There he played a major role for the specific mission of this institute; namely, to combine fundamental research with more applied work in direct connection with industry, thereby cross-fertilising both domains of activity. His field of interest is numerical optimization which he has applied to various areas including fluid mechanics, molecular design, geophysics, optimal control, and production management. He is known for his works in nonsmooth optimization and, more generally, the use of convex analysis for the development of practical optimization tools. He was awarded the Dantzig Prize of the Mathematical Programming Society in 1994.

## Abridged curriculum of Claude Lemaréchal

- French; born April 1st 1944 in Paris.

- 1967: “Ingénieur” in Applied Mathematics, Ecole Nationale Supérieure d’Electrotechnique, d’Informatique, d’Hydraulique de Toulouse.

- 1969: “Docteur-lngénieur”, University of Toulouse.

- 1980: “Docteur ès Sciences Mathématiques”, University of Paris IX.

- Present address: Institut National de Recherche en Informatique et Automatique, 655 avenue de l’Europe, 38330 Montbonnot, France.

- Former head of the Research Project Teamss “Théorie des Systems”, “Programmation Mathématique”, “Optimisation Numérique”.

- Professor at the University of Paris 1 from 1994 to 1997.

- Professor at École Nationale Supérieure d’Ingénieurs en Mathématiques Appliquées de Grenoble from 1999 to 2006.

- Dantzig Prize 1994.

Internationally known for his works in numerical optimization, especially nonsmooth optimization, and its applications in different areas such as: fluid mechanics, optimum design, crystallography, operations research, etc.

Former associate editor of: SIAM Journal on Control and Optimization, SIAM Journal on Optimization; Mathematical Programming; Contrôle, Optimisation, et Calcul Variationnel.

Participates actively to the development of mathematical methods in various branches of industry; particularly significant results in meteorology, electrical production.

Consultant in various applied domains where optimization is needed
(production management, networking, finance, geophysics, *etc.*).

### publications

Author of over 50 publications in international journals; some of the most significant ones are:

- Nonsmooth Optimization. Proceedings, Pergamon Press (1978) (with R. Mifflin).
- Convex Analysis and Minimization Algorithms. Springer Verlag, Grundlehren 305, 306 (1993) (with J.B. Hiriart-Urruty).
- Fundamentals of Convex Analysis. Springer Verlag, Grundlehren Text Editions (2001) (with J.B. Hiriart-Urruty).
- Numerical Optimisation: Theoretical and Practical Aspects. Springer Verlag, Universitext (2003) (with J.F. Bonnans, J. Ch. Gilbert, C. Sagastizábal).
- An algorithm for minimizing convex functions. Proceedings, Information Processing ’74, Stockholm (1974).
- Practical aspects of the Moreau-Yosida regularization: theoretical preliminaries. SIAM Journal on Optimization 7,2 (1997) 367-385 (with C. Sagastizábal).
- Variable metric bundle methods: from conceptual to implementable forms. Mathematical Programming 76,3 (1997), pp. 393-410 (with C. Sagastizábal).
- The U-Lagrangian af a convex function. Transactions of the AMS 352,2 (2000), pp. 711-729 (with F. Oustry and C. Sagastizábal).
- Lagrangian relaxation. in: Computational Combinatorial Optimization, M. Jünger, D. Naddef (eds.) Springer Verlag (2001), pp. 112-156.
- A primal-proximal heuristic applied to the French unit-commitment problem. Mathematical Programming 104,1 (2005) pp. 129-152 (with L. Dubost, R. Gonzalez).
- On the equivalence between complementarity systems, projected systems and differential inclusions. Systems and Control Letters 55 (2005), pp. 45-51 (with V. Acary, B. Brogliato, A. Daniilidis).
- A convex-analysis perspective on disjunctive cuts. Mathematical Programming 106,3 (2006) pp. 567-586 (with G. Cornuéjols).
- Comparison of bundle and classical column generation. To appear in Mathematical Programming (with O. Briant, Ph. Meurdesoif, S. Michel, N. Perrot, F. Vanderbeck).
- An inexact conic buncle variant suited to column generation. To appear in Mathematical Programming (with K.C. Kiwiel).
- A bundle-type algorithm for routing in telecommunication data networks. To appear in Computational Optimization and Applications (with A. Ouorou, G. Petrou).

### research

Current research interests concern mainly convex analysis and nonsmooth optimization; they can be divided into three categories:

- Second-order approximation of convex functions, along the lines of Ref. 8 above; this is a prerequisite to developing really fast nonsmooth optimization algorithms;

- Developing optimization software, with application to large-scale decomposable problems (see Refs. 6, 7, 10);

- Establishing real communication with combinatorial optimization (Refs. 9, 12, 13), and also with nonsmooth dynamics (Ref. 11).