Metric Regularity in Convex Semi-Infinite Optimization under Canonical Perturbations

نویسندگان

  • María J. Cánovas
  • Diethard Klatte
  • Marco A. López
  • Juan Parra
چکیده

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the Slater constraint qualification, together with a certain additional requirement in the Karush-Kuhn-Tucker conditions. For linear problems this sufficient condition turns out to be also necessary for the metric regularity, and it is equivalent to some well-known stability concepts. METRIC REGULARITY IN CONVEX SEMI-INFINITE OPTIMIZATION UNDER CANONICAL PERTURBATIONS∗ M.J. CÁNOVAS† , D. KLATTE‡ , M.A. LÓPEZ§ , AND J. PARRA† Abstract. This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the Slater constraint qualification, together with a certain additional requirement in the Karush-Kuhn-Tucker conditions. For linear problems this sufficient condition turns out to be also necessary for the metric regularity, and it is equivalent to some well-known stability concepts.

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عنوان ژورنال:
  • SIAM Journal on Optimization

دوره 18  شماره 

صفحات  -

تاریخ انتشار 2007