A power penalty method for second-order cone linear complementarity problems

We propose a power penalty method for solving the second-order cone linear complementarity problems (SOCLCPs), which is an extension of Wang and Yang’s research (Wang and Yang, 2008). Using this method, the SOCLCP is converted to asymptotic power penalty equations (PPEs). We prove that the solution sequence of the asymptotic PPEs converges to the solution of the SOCLCP at an exponential rate under a mild assumption. Numerical results are reported to examine the efficiency of the proposed method.