- Title
- Metric Regularity of the Sum of Multifunctions and Applications
- Creator
- Van Ngai, Huynh; Tron, Nguyen Tron; Thera, Michel
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/55801
- Identifier
- vital:5796
- Identifier
-
https://doi.org/10.1007/s10957-013-0385-6
- Identifier
- ISSN:1573-2878
- Abstract
- The metric regularity of multifunctions plays a crucial role in modern variational analysis and optimization. This property is a key to study the stability of solutions of generalized equations. Many practical problems lead to generalized equations associated to the sum of multifunctions. This paper is devoted to study the metric regularity of the sum of multifunctions. As the sum of closed multifunctions is not necessarily closed, almost all known results in the literature on the metric regularity for one multifunction (which is assumed usually to be closed) fail to imply regularity properties of the sum of multifunctions. To avoid this difficulty, we use an approach based on the metric regularity of so-called epigraphical multifunctions and the theory of error bounds to study the metric regularity of the sum of two multifunctions, as well as some related important properties of variational systems. Firstly, we establish the metric regularity of the sum of a regular multifunction and a pseudo-Lipschitz multifunction with a suitable Lipschitz modulus. These results subsume some recent results by Durea and Strugariu. Secondly, we derive coderivative characterizations of the metric regularity of epigraphical multifunctions associated with the sum of multifunctions. Applications to the study of the behavior of solutions of variational systems are reported. © 2013 Springer Science+Business Media New York.
- Publisher
- Springer New York LLC
- Relation
- Journal of Optimization Theory and Applications Vol. 160, no. 2 (2014), p. 355-390; http://purl.org/au-research/grants/arc/DP110102011
- Rights
- Copyright Springer Science
- Rights
- This metadata is freely available under a CCO license
- Subject
- Coderivative; Error bound; Metric regularity; Pseudo-Lipschitz property; Sum-stability; Variational systems; 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0906 Electrical and Electronic Engineering
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