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
- Full Text:
- Reviewed:
- 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.
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
- Full Text:
- Reviewed:
- 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.
Directional metric regularity of multifunctions
- Authors: Ngai, Huynh Van , Thera, Michel
- Date: 2015
- Type: Text , Journal article
- Relation: Mathematics of Operations Research Vol. 40, no. 4 (2015), p. 969-991
- Relation: http://purl.org/au-research/grants/arc/DP110102011
- Full Text:
- Reviewed:
- Description: In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by using the relative lower semicontinuous envelopes of the distance functions to set-valued mappings. We then apply these characterizations to establish a coderivative type criterion for directional metric regularity as well as for the robustness of metric regularity.
- Description: In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by using the relative lower semicontinuous envelopes of the distance functions to set-valued mappings. We then apply these characterizations to establish a coderivative type criterion for directional metric regularity as well as for the robustness of metric regularity. © 2015 INFORMS.