Smooth-like lower order penalty approach for solving second-order cone mixed complementarity problems

Abstract

In this paper, a smooth-like lower order penalty approach is proposed for solving second-order cone mixed complementarity problems (SOCMCPs), which is closely related to second-order cone programming. Four kinds of special smoothing functions are considered in this approach. In light of this approach, the SOCMCP is approximated by asymptotic smooth-like lower order penalty equations (SLOPEs) with penalty parameter and smoothing parameter. Under a mild assumption, the main result shows that the solution sequence of the asymptotic SLOPEs converges exponentially to the solution of the SOCMCP while the penalty parameter tends to positive infinity and the smoothing parameter monotonically decreases to zero. A corresponding algorithm is constructed and the numerical experimental results are reported to illustrate the feasibility of the proposed algorithm. The performance profile of four specific smoothing functions is presented, and the numerical performance comparison of the proposed approach with other three algorithms is also investigated.