Claude Lemaréchal is a French applied mathematician, and former senior researcher (''directeur de recherche'') at

INRIA The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name French Institute for Research in Comp ...

near

Grenoble Grenoble ( ; ; or ; or ) is the Prefectures in France, prefecture and List of communes in France with over 20,000 inhabitants, largest city of the Isère Departments of France, department in the Auvergne-Rhône-Alpes Regions of France, region ...

, France. In

mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...

, Claude Lemaréchal is known for his work in

numerical methods Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods t ...

for nonlinear optimization, especially for problems with nondifferentiable kinks. Lemaréchal and Philip Wolfe pioneered

bundle method Subgradient methods are convex optimization methods which use Subderivative, subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s, subgradient methods are convergent when applied even to a non-differentiable object ...

s of descent for convex minimization.Citation of Claude Lemaréchal
for the George Dantzig Prize in 1994 in ''Optima'', Issue 44 (1994) pages 4-5.

Awards

In 1994, Claude Lemaréchal and Roger J-B Wets were each awarded the George B. Dantzig Prize. Recognizing "original research that has had a major impact on the field of mathematical programming", the Dantzig Prize is awarded by the Society for Industrial and Applied Mathematics (SIAM) and the Mathematical Programming Society (MPS).

Lagrangian duality and nonconvex primal problems

Soon after joining

(then named " IRIA"), Lemaréchal had the assignment of helping a glass-manufacturer with a problem of scheduling its production, a problem whose first formulation required minimizing a non-convex function. For this non-convex minimization problem, Lemaréchal applied the theory of Lagrangian duality that was described in Lasdon's ''Optimization Theory for Large Systems''. Because the primal problem was non-convex, there was no guarantee that a solution to the dual problem would provide useful information about the primal. Nonetheless, the dual problem did furnish useful information. Lemaréchal's success with Lagrangian dual methods on nonlinear programming problems with nonconvexities interested Ivar Ekeland and Jean–Pierre Aubin, who applied the Shapley–Folkman lemma to explain Lemaréchal's success. * Page 373: * Page 373: The Aubin–Ekeland analysis of duality gaps considered the ''

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

'' closure of a nonconvex minimization problem — that is, the problem defined by the closed

hull of the epigraph of the original problem. Following Ekeland and Aubin, similar applications of the Shapley–Folkman lemma are described in optimization monographs and textbooks. * See Figure 5.1.9 (page 496): * Pages 267–279: These developments were catalyzed by Lemaréchal's demonstration that Lagrangian-dual methods were useful on some

optimization problem In mathematics, engineering, computer science and economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goo ...

s that lacked convexity.

Bundle methods of descent

Lemaréchal's research also led to his work on ( conjugate) subgradient methods and on bundle methods of descent for convex minimization problems.

Notes

Bibliography

Biographical

*
Citation of Claude Lemaréchal
for the George Dantzig Prize in 1994 in ''Optima'', Issue 44 (1994) pages 4–5.

Scientific publications

* * ** ** * * {{DEFAULTSORT:Lemarechal, Claude Numerical analysts French mathematical analysts French operations researchers Theoretical computer scientists 20th-century French mathematicians 21st-century French mathematicians French computer scientists Living people Year of birth missing (living people)