Solving Symmetric and Positive Definite Second-Order Cone Linear Complementarity Problem by A Rational Krylov Subspace Method

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