Optimal transport, shape optimization and global minimization

Bijan Mohammadi

doi:10.1016/j.crma.2007.03.015

Numerical Analysis

Optimal transport, shape optimization and global minimization
[Transport optimal généralisé, optimisation de formes et minimisation globale]

Présenté par : Olivier Pironneau

Bijan Mohammadi ¹

¹ Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France

Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 591-596.

Résumé
Abstract

Nous présentons la résolution de problème de transport optimal généralisé comme solution d'une minimisation globale basée sur la solution de problèmes à valeurs aux limites. On s'intéresse au cas de second membre à signe variable dans l'équation de Monge–Ampère, avec comme application l'optimisation de formes de surfaces à courbure donnée. Les problèmes ont toujours des minima locaux mais l'optimum global est unique.

We present the numerical solution of general optimal transport problems through global minimization formulated as solution of boundary value problems. The paper is not on optimal transport but aims to show that the optimization problem behind needs global solutions. One gives also interest to the variable sign right-hand-side case with application to shape optimization for surfaces at given curvature. Both the positive and variable sign problems have local minima, but have unique global solution.

Reçu le : 2006-11-07
Accepté le : 2007-03-14
Publié le : 2007-05-01

DOI : 10.1016/j.crma.2007.03.015

Affiliations des auteurs :

Bijan Mohammadi ¹

¹ Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France

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Bijan Mohammadi. Optimal transport, shape optimization and global minimization. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 591-596. doi : 10.1016/j.crma.2007.03.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.015/

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