Numerical Analysis
Optimal transport, shape optimization and global minimization
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 591-596.

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.

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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2007.03.015
Mohammadi, Bijan 1

1 Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France
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Mohammadi, Bijan. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.03.015/

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