On Properties of the Bilinear Penalty Function Method for Mathematical Programs with Semidefinite Cone Complementarity Constraints

摘要

This paper is devoted to the study of properties of the bilinear penalty function method for the mathematical programs with semidefinite cone complementarity constraints(SDCMPCC), in which the complementarity constraint appears as a bilinear penalty term in the objective. We discuss the relationships of solutions between the SDCMPCC and its bilinear penalty problem as well as the second order sufficient conditions and the constraint qualifications between these two problems. Moreover, under certain conditions, we demonstrate that any accumulation point of the sequence generated by the bilinear penalty function method is an S-stationary point of the SDCMPCC.