A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem

Jia Wu, Yi Zhang (), Liwei Zhang () and Yue Lu ()
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Jia Wu: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Yi Zhang: Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai 200237, P. R. China
Liwei Zhang: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Yue Lu: School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2016, vol. 33, issue 04, 1-26

Abstract: This paper is devoted to the study of solving method for a type of inverse linear semidefinite 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.

Keywords: Inverse linear semidefinite programming problems; mathematical program with semidefinite cone complementarity constraints; penalty methods; sequential convex program (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0217595916500251

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