文献类型：期刊文献

英文题名：A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem

作者：Wu, Jia[1];Zhang, Yi[2];Zhang, Liwei[1];Lu, Yue[3]

机构：[1]Dalian Univ Technol, Sch Math Sci, Inst Operat Res & Control Theory, Dalian 116024, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Sch Sci, Shanghai 200237, Peoples R China;[3]Tianjin Normal Univ, Sch Math Sci, Tianjin 300387, Peoples R China

年份：2016

卷号：33

期号：4

外文期刊名：ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH

收录：;EI(收录号：20163002647352);WOS:【SCI-EXPANDED(收录号:WOS:000383051400003)】；

基金：We would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper. The research is supported by the National Natural Science Foundation of China (Nos. 11301049, 11401210, 11571059 and 91330206), the Fundamental Research Funds for the Central Universities (No. DUT15LK32), and the Doctoral Foundation of Tianjin Normal University (No. 52XB1513).

语种：英文

外文关键词：Inverse linear semidefinite programming problems; mathematical program with semidefinite cone complementarity constraints; penalty methods; sequential convex program

摘要：This paper is devoted to the study of solving method for a type of inverse linear semi-definite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is actually a nonsmooth DC programming problem which can be solved by a sequential convex program approach. Convergence analysis of the penalty models and the sequential convex program approach are shown. Numerical results are reported to demonstrate the efficiency of our approach.