Metric Regularity in Convex Semi-Infinite Optimization under Canonical Perturbations
M. J. Cánovas, Diethard Klatte, Marco A. López, Juan Parra · SIAM Journal on Optimization · 2007
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.