Generalized lower-order penalty algorithm for solving second-order cone mixed complementarity problems

Abstract

The second-order cone mixed complementarity problems (SOCMCPs) can directly present the KKT conditions of the second-order cone programming, and have broad range of applications. We establish the generalized lower-order penalty algorithm in this article for solving the SOCMCPs. By using the proposed algorithm, the SOCMCP is converted to asymptotic lower-order penalty equations (LOPEs). Under the assumption that the involved function possesses the ξ-monotone, we show that when the penalty parameter tends to positive infinity, the solution sequence of the asymptotic LOPEs converges to the solution of the SOCMCP at an exponential rate. Numerical results are reported to examine the efficiency of the proposed algorithm.