Comptes Rendus
no. 3
The legacy of Jean-Jacques Moreau in mechanics
A duality recipe for non-convex variational problems
[Un principe de dualité pour des problèmes variationnels non convexes]
Guy Bouchitté1  ; Minh Phan1
1 Institut de mathématiques, Université de Toulon, 83957 La Garde cedex, France
Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 206-221.

Nous présentons un principe général de convexification permettant de traiter certains problèmes variationnels non convexes. Ce principe permet de mettre en œuvre les puissantes techniques de dualité en ramenant de tels problèmes à des formulation de type primal–dual. Quelques perspectives et problèmes ouverts sont évoqués.

The aim of this paper is to present a general convexification recipe that can be useful for studying non-convex variational problems. In particular, this allows us to treat such problems by using a powerful primal–dual scheme. Possible further developments and open issues are given.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2017.12.011
Keywords: Non-convex optimization, Min–Max principle, Free boundary, Free discontinuities, Γ-convergence
Mot clés : Optimisation non convexe, Principe de min–max, Frontière libre, Discontinuités libres, Γ-convergence
Guy Bouchitté 1 ; Minh Phan 1

1 Institut de mathématiques, Université de Toulon, 83957 La Garde cedex, France 
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Guy Bouchitté; Minh Phan. A duality recipe for non-convex variational problems. Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 206-221. doi : 10.1016/j.crme.2017.12.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.011/

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