Exact formula for the second-order tangent set of the second-order cone complementarity sET^∗

Chen, Jein-Shan1; Ye, Jane J.2; Zhang, Jin3; Zhou, Jinchuan4

2019

10.1137/17M1140479

SIAM JOURNAL ON OPTIMIZATION   影响因子和分区

1052-6234

1095-7189

The second-order tangent set is an important concept in describing the curvature of the set involved. Due to the existence of the complementarity condition, the second-order cone (SOC) complementarity set is a nonconvex set. Moreover, unlike the vector complementarity set, the SOC complementarity set is not even the union of finitely many polyhedral convex sets. Despite these difficulties, we succeed in showing that like the vector complementarity set, the SOC complementarity set is second-order directionally differentiable and an exact formula for the second-order tangent set of the SOC complementarity set can be given. We derive these results by establishing the relationship between the second-order tangent set of the SOC complementarity set and the second-order directional derivative of the projection operator over the SOC, and calculating the second-order directional derivative of the projection operator over the SOC. As an application, we derive second-order necessary optimality conditions for the mathematical program with SOC complementarity constraints.
Copyright © by SIAM.

projection operator second-order directional derivatives second-order tangent sets second-order cone complementarity sets second-order necessary optimality conditions mathematical program with second-order cone complementarity constraints

EI ; SCI

英语

其他

Ministry of Science and Technology, Taiwan[] ; Natural Sciences and Engineering Research Council of Canada[11601458] ; National Natural Science Foundation of China[11771255] ; National Natural Science Foundation of China[11801325] ; Natural Sciences and Engineering Research Council of Canada[11971220]

Mathematics

Mathematics, Applied

WOS:000546996000022

Society for Industrial and Applied Mathematics Publications

20195007823053

Application programs ; Set theory

Computer Software, Data Handling and Applications:723 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

MATHEMATICS

EV Compendex

1.Department of Mathematics, National Taiwan Normal University, Taipei; 11677, Taiwan
2.Department of Mathematics and Statistics, University of Victoria, Victoria; B.C.; V8W 2Y2, Canada
3.Department of Mathematics, Southern University of Science and Technology, Shenzhen, China
4.Department of Statistics, School of Mathematics and Statistics, Shandong University of Technology, Zibo; 255049, China

Chen, Jein-Shan,Ye, Jane J.,Zhang, Jin,et al. Exact formula for the second-order tangent set of the second-order cone complementarity sET^∗[J]. SIAM JOURNAL ON OPTIMIZATION,2019,29(4):2986-3011.

Chen, Jein-Shan,Ye, Jane J.,Zhang, Jin,&Zhou, Jinchuan.(2019).Exact formula for the second-order tangent set of the second-order cone complementarity sET^∗.SIAM JOURNAL ON OPTIMIZATION,29(4),2986-3011.

Chen, Jein-Shan,et al."Exact formula for the second-order tangent set of the second-order cone complementarity sET^∗".SIAM JOURNAL ON OPTIMIZATION 29.4(2019):2986-3011.