Sur les programmes convexes définis dans des espaces vectoriels topologiques
Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 457-491.

On étudie les conditions d’optimalité et la dualité pour des programmes convexes : sup{f(x)|g(x)≤0} où f est une fonction numérique concave définie dans un espace vectoriel topologique réel E localement convexe séparé, et où g est une application convexe d’une partie de E dans un espace vectoriel topologique localement convexe séparé et ordonné G. On définit à cet effet les sous-différentiels et la fonction conjuguée d’une fonction vectorielle à valeurs dans G. On introduit également les ensembles et fonctions localement convexes définis dans un espace localement convexe. On obtient ainsi diverses extensions de résultats connus en programmation convexe.

We study optimally conditions and duality for convex programs : sup{f(x)|g(x)≤0} where f is a concave real-valued function which is defined on a subset of a real locally convex Hausdorff topological vector space E, and where g is a convex mapping of a subset of E into a real locally convex Hausdorff ordered topological vector space G. For this purpose, we define subdifferentials and a conjugate function of a G-valued function. We also introduce locally convex subsets and locally convex functions defined on a locally convex topological vector space. We obtain, in this way, several extensions of well-known results in convex programming.

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Raffin, Claude. Sur les programmes convexes définis dans des espaces vectoriels topologiques. Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 457-491. doi : 10.5802/aif.347. https://www.numdam.org/articles/10.5802/aif.347/

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