Stability Results of Variational Systems Under Openness with Respect to Fixed Sets

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• 作者：M. Bianchi (1)
  G. Kassay (2)
  R. Pini (3)
  
  1. Universit脿 Cattolica del Sacro Cuore ; Milano ; Italy
  2. Babe艧-Bolyai University ; Cluj ; Romania
  3. Universit脿 degli Studi di Milano-Bicocca ; Milano ; Italy
  
• 关键词：Linear openness ; Metric regularity ; Sum of maps ; Generalized equation ; Sensitivity analysis ; Fixed point theorem ; Ekeland鈥檚 variational principle ; 49J53 ; 49K40 ; 90C31
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：164
• 期：1
• 页码：92-108
• 全文大小：222 KB
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• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

In this paper, we present the notions of openness and metric regularity for a set-valued map with respect to two fixed sets, proving their equivalence. By using different approaches, we show the stability, with respect to the sum of maps, of the openness property, both in the setting of Banach spaces and of metric spaces. Finally, we infer the regularity of the map solving a generalized parametric equation defined via a parametric map that is, in its turn, perturbed by the sum with another map.