Narrow Results

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.

In this paper, we shall concern with the existence result of unilateral parabolic degenerated problems associated to the equations of the form

The proof is based on the penalty methods.