Cánovas Cánovas, María Josefa, Hantoute, Abderrahim, López Cerdá, Marco A., Parra López, Juan
Lipschitz behavior of convex semi-infinite optimization problems: a variational approach
Journal of Global Optimization. 2008, 41(1): 1-13. doi:10.1007/s10898-007-9205-6
URI: http://hdl.handle.net/10045/75118
DOI: 10.1007/s10898-007-9205-6
ISSN: 0925-5001 (Print)
Abstract: 
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.
Keywords:Convex semi-infinite programming, Metric regularity, Optimal set, Lipschitz modulus
Springer Science+Business Media, LLC
info:eu-repo/semantics/article