Directional Holder metric regularity
- Authors: Ngai, Huynh Van , Tron, Nguyen Huu , Thera, Michel
- Date: 2016
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 171, no. 3 (2016), p. 785-819
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- Description: This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Holder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Holder/Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.
Slopes of multifunctions and extensions of metric regularity
- Authors: Ngai, Huynh Van , Kruger, Alexander , Thera, Michel
- Date: 2012
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics (Tạp chí toán học) Vol. 40, no. 2/3 (2012), p. 355-369
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.