Mathematical Programs with Second-Order Cone Complementarity Constraints: Strong Stationarity and Approximation Method

Zhu, Xide1,2; Zhang, Jin3; Zhou, Jinchuan4; Yang, Xinmin5

2019-05

10.1007/s10957-018-01464-w

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   影响因子和分区

0022-3239

1573-2878

The existence of complementarity constraints causes the difficulties for studying mathematical programs with second-order cone complementarity constraints, since the standard constraint qualification, such as Robinson's constraint qualification, is invalid. Therefore, various stationary conditions including strong, Mordukhovich and Clarke stationary conditions have been proposed, according to different reformulations of the second-order cone complementarity constraints. In this paper, we present a new reformulation of this problem by taking into consideration the Jordan algebra associated with the second-order cone. It ensures that the classical Karush-Kuhn-Tucker condition coincides with the strong stationary condition of the original problem. Furthermore, we propose a class of approximation methods to solve mathematical programs with second-order cone complementarity constraints. Any accumulation point of the iterative sequences, generated by the approximation method, is Clarke stationary under the corresponding linear independence constraint qualification. This stationarity can be enhanced to strong stationarity with an extra strict complementarity condition. Preliminary numerical experiments indicate that the proposed method is effective.

Mathematical programs with second-order cone complementarity constraints Stationarity conditions Jordan product Calmness conditions Approximation methods

SCI

英语

通讯

Shandong Province Natural Science Foundation[ZR2016AM07]

Operations Research & Management Science ; Mathematics

Operations Research & Management Science ; Mathematics, Applied

WOS:000464757100009

SPRINGER/PLENUM PUBLISHERS

ENGINEERING

Web of Science

1.Shanghai Univ, Sch Management, Shanghai 200444, Peoples R China
2.Yokohama Natl Univ, Fac Business Adm, Hodogaya Ku, 79-4 Tokiwadai, Yokohama, Kanagawa 2408501, Japan
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518000, Peoples R China
4.Shandong Univ Technol, Sch Math & Stat, Dept Stat, Zibo 255049, Peoples R China
5.Chongqing Normal Univ, Coll Math Sci, Chongqing 401131, Peoples R China

Zhu, Xide,Zhang, Jin,Zhou, Jinchuan,et al. Mathematical Programs with Second-Order Cone Complementarity Constraints: Strong Stationarity and Approximation Method[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2019,181(2):521-540.

Zhu, Xide,Zhang, Jin,Zhou, Jinchuan,&Yang, Xinmin.(2019).Mathematical Programs with Second-Order Cone Complementarity Constraints: Strong Stationarity and Approximation Method.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,181(2),521-540.

Zhu, Xide,et al."Mathematical Programs with Second-Order Cone Complementarity Constraints: Strong Stationarity and Approximation Method".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 181.2(2019):521-540.