An extended conjugate duality for generalized semi-infinite programming problems via a convex decomposition

A. Aboussoror (1) , Samir Adly (2) , S Salim (1)

1 Faculté Polydisciplinaire de Safi
2 XLIM-MATHIS - Mathématiques & Sécurité de l'information

We present an extended conjugate duality for a generalized semi-infinite programming problem (P). The extended duality is defined in the context of the absence of convexity of problem (P), by means of a decomposition into a family of convex subproblems and a conjugate dualization of the subproblems. Under appropriate assumptions, we establish strong extended duality and provide necessary and sufficient optimality conditions for problem (P). These extended conjugate duality and optimality conditions are new in the literature of generalized semi-infinite programming .

Mots clés: Generalized semi-infinite programming; reverse convex problems; DC problems; convex analysis; conjugate duality

Domaines: Optimisation et contrôle [math.OC]

A. Aboussoror, Samir Adly, S Salim. An extended conjugate duality for generalized semi-infinite programming problems via a convex decomposition. Optimization, In press, ⟨10.1080/02331934.2019.1655739⟩. ⟨hal-02433103⟩