Claude Lemaréchal is a French applied mathematician, and former senior researcher (directeur de recherche) at INRIAINRIA is the acronym for the National Institute for Research in Computer Science and Control, in the original French, Institut national de recherche en informatique et en automatique (INRIA). near Grenoble, France.
In mathematical optimization, Claude Lemaréchal is known for his work in numerical methods for nonlinear optimization, especially for problems with nondifferentiable kinks. Lemaréchal and Philip Wolfe pioneered bundle methods 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 INRIA (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 experiments were discussed in later publications: 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 closure of a nonconvex minimization problem — that is, the problem defined by the closed convex hull of the epigraph of the original problem. Following Ekeland and Aubin, similar applications of the Shapley–Folkman lemma are described in optimization monographs Besides presenting Ekeland-style analysis of duality gaps (acknowledgment on page 381), Bertsekas (1982) applies Lagrangian dual methods to the scheduling of electrical power plants ("unit commitment problems"), where nonconvexity appears because of integer constraints: 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 problems 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