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

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.
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• HAL Id : inria-00074271, version 1

### Citation

J. Frederic Bonnans, Roberto Cominetti. Perturbed optimization in Banach spaces III: Semi-infinite optimization. [Research Report] RR-2404, INRIA. 1994. ⟨inria-00074271⟩

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