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2Abstract subdifferential
2Coderivative
2Directional Hölder metric subregularity
2Metric subregularity
2Slope
10101 Pure Mathematics
10102 Applied Mathematics
10103 Numerical and Computational Mathematics
10802 Computation Theory and Mathematics
1Asplund space
1Directional metric pseudo-subregularity
1Distance functions
1Error bound
1Error bound property
1Fréchet normal cone
1Fréchet subdifferential
1Generalized Equations
1Generalized equations

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Directional metric regularity of multifunctions

- Ngai, Huynh Van, Thera, Michel

**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.

**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.

Metric regularity relative to a cone

- Van Ngai, Huynh, Tron, Nguyen, Théra, Michel

**Authors:**Van Ngai, Huynh , Tron, Nguyen , Théra, Michel**Date:**2019**Type:**Text , Journal article**Relation:**Vietnam Journal of Mathematics Vol. 47, no. 3 (2019), p. 733-756**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:**false**Reviewed:****Description:**The purpose of this paper is to discuss some of the highlights of the theory of metric regularity relative to a cone. For example, we establish a slope and some coderivative characterizations of this concept, as well as some stability results with respect to a Lipschitz perturbation.

Directional metric pseudo subregularity of set-valued mappings: a general model

- Van Ngai, Huynh, Tron, Nguyen, Van Vu, Nguyen, Théra, Michel

**Authors:**Van Ngai, Huynh , Tron, Nguyen , Van Vu, Nguyen , Théra, Michel**Date:**2020**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 61-87**Full Text:**false**Reviewed:****Description:**This paper investigates a new general pseudo subregularity model which unifies some important nonlinear (sub)regularity models studied recently in the literature. Some slope and abstract coderivative characterizations are established. © 2019, Springer Nature B.V.

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