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](_blank)
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
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 ...
(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 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 ...
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 Lemaréchalfor the
George Dantzig Prize in 1994 in ''Optima'', Issue 44 (1994) pages 4–5.
Scientific publications
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{{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)