Solving symmetric and positive definite second-order cone linear complementarity problem by a rational Krylov subspace method

Abstract

The second-order cone linear complementarity problem (SOCLCP) is a generalization of the classical linear complementarity problem. It has been known that SOCLCP, with the globally uniquely solvable property, is essentially equivalent to a zero-finding problem in which the associated function bears much similarity to the transfer function in model reduction [38]. In this paper, we propose a new rational Krylov subspace method to solve the zero-finding problem for the symmetric and positive definite SOCLCP. The algorithm consists of two stages: first, it relies on an extended Krylov subspace to obtain an approximation of the zero root, and then applies multiple-pole rational Krylov subspace projections iteratively to acquire an accurate solution. Numerical evaluations on various types of SOCLCP examples demonstrate its efficiency and robustness.