Perturbed optimization in Banach spaces III: Semi-infinite optimization

: This paper is devoted to the study of perturbed semi-infinite optimization problems, i.e. minimization over IR n with an infinite number of inequality constraints. We obtain the second order expansion of the optimal value function and the first order expansion of approximate optimal solutions in two cases: (i) when the number of binding constraints is finite, and (ii) when the inequality constraints are parametrized by a real scalar. These results are partly obtained by specializing the sensitivity theory for perturbed optimization developed in part I (cf. [4]), and deriving specific sharp lower estimates for the optimal value function which take into account the curvature of the positive cone in the space C(\Omega\Gamma of continuous real-valued functions. (R'esum'e : tsvp) Email: Frederic.Bonnans@inria.fr Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile. Partially supported by Fondecyt 1940564 Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencou..