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

Indexed by:Journal Article

Date of Publication:2016-08-01

Journal:ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH

Included Journals:Scopus、EI、SCIE

Volume:33

Issue:4

ISSN:0217-5959

Key Words:Inverse linear semidefinite programming problems; mathematical program with semidefinite cone complementarity constraints; penalty methods; sequential convex program

Abstract: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.