Directional quasi-/pseudo-normality as sufficient conditions for metric subregularity^∗

Bai, Kuang1; Ye, Jane J.1; Zhang, Jin2

2019

10.1137/18M1232498

SIAM JOURNAL ON OPTIMIZATION   影响因子和分区

1052-6234

1095-7189

In this paper we study sufficient conditions for metric subregularity of a set-valued map which is the sum of a single-valued continuous map and a locally closed subset. First we derive a sufficient condition for metric subregularity which is weaker than the so-called first-order sufficient condition for metric subregularity (FOSCMS) by adding an extra sequential condition. Then we introduce directional versions of quasi-normality and pseudo-normality which are stronger than the new weak sufficient condition for metric subregularity but weaker than classical quasi-normality and pseudo-normality. Moreover we introduce a nonsmooth version of the second-order sufficient condition for metric subregularity and show that it is a sufficient condition for the new sufficient condition for metric subregularity to hold. An example is used to illustrate that directional pseudo-normality can be weaker than FOSCMS. For the class of set-valued maps where the single-valued mapping is affine and the abstract set is the union of finitely many convex polyhedral sets, we show that pseudo-normality and hence directional pseudo-normality holds automatically at each point of the graph. Finally we apply our results to complementarity and Karush–Kuhn–Tucker systems.
Copyright © by SIAM.

directional limiting normal cones metric subregularity calmness error bounds directional pseudo-normality directional quasi-normality complementarity systems

EI ; SCI

英语

其他

Natural Sciences and Engineering Research Council of Canada[11601458] ; Natural Sciences and Engineering Research Council of Canada[11871269] ; Natural Sciences and Engineering Research Council of Canada[11971220]

Mathematics

Mathematics, Applied

WOS:000546996000010

Society for Industrial and Applied Mathematics Publications

20195007817568

Error analysis

Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

MATHEMATICS

EV Compendex

1.Department of Mathematics and Statistics, University of Victoria, BC; V8W 2Y2, Canada
2.Department of Mathematics, Southern University of Science and Technology, Shenzhen, China

Bai, Kuang,Ye, Jane J.,Zhang, Jin. Directional quasi-/pseudo-normality as sufficient conditions for metric subregularity^∗[J]. SIAM JOURNAL ON OPTIMIZATION,2019,29(4):2625-2649.

Bai, Kuang,Ye, Jane J.,&Zhang, Jin.(2019).Directional quasi-/pseudo-normality as sufficient conditions for metric subregularity^∗.SIAM JOURNAL ON OPTIMIZATION,29(4),2625-2649.

Bai, Kuang,et al."Directional quasi-/pseudo-normality as sufficient conditions for metric subregularity^∗".SIAM JOURNAL ON OPTIMIZATION 29.4(2019):2625-2649.