# Perturbed optimization in Banach spaces III: Semi-infinite optimization

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1 PROMATH - Mathematical Programming Inria Paris-Rocquencourt

Abstract : This paper is devoted to the study of perturbed semi-infinite optimization problems, i.e. minimization over \$\er^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. \citebc1, 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\$ of continuous real-valued functions.

Keywords : SEMI-INFINITE PROGRAMMING EPILIMITS APPROXIMATE SOLUTIONS DIRECTIONAL CONSTRAINT QUALIFICATION SENSITIVITY ANALYSIS MARGINAL FUNCTION

Autor: J. Frederic Bonnans - Roberto Cominetti

Fuente: https://hal.archives-ouvertes.fr/

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