Variational pairs and applications to stability in nonsmooth analysis
Nonlinear Analysis: Theory, Methods & Applications
Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications)
Metric Regularity in Convex Semi-Infinite Optimization under Canonical Perturbations
SIAM Journal on Optimization
Minimizing Convex Functions with Bounded Perturbations
SIAM Journal on Optimization
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In this paper we make use of subdifferential calculus and other variational techniques, traced out from [Ioffe, A.D.: Metric regularity and subdifferential calculus. Uspekhi Mat. Nauk 55, 3(333), 103---162; Engligh translation Math. Surveys 55, 501---558 (2000); Ioffe, A.D.: On rubustness of the regularity property of maps. Control cybernet 32, 543---554 (2003)], to derive different expressions for the Lipschitz modulus of the optimal set mapping of canonically perturbed convex semi-infinite optimization problems. In order to apply this background for obtaining the modulus of metric regularity of the associated inverse multifunction, we have to analyze the stable behavior of this inverse mapping. In our semi-infinite framework this analysis entails some specific technical difficulties. We also provide a new expression of a global variational nature for the referred regularity modulus.