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 $\xi$-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.

二阶锥混合互补问题（SOCMCPs）可以直接表示二阶锥编程的KKT条件，具有广泛的应用范围。在本文中，我们建立了广义的低阶惩罚算法来求解SOCCMP。通过使用所提出的算法，将SOCMCP转换为渐近的低阶惩罚方程（LOPEs）。假设所涉及的功能具有$\xi$-单调，我们表明当惩罚参数趋于正无穷大时，渐近LOPE的解序列以指数速率收敛到SOCMCP的解。数值结果被报道以检验所提出算法的效率。