Linear complementarity problems on extended second order cones

TL;DR

This paper investigates linear complementarity problems on extended second order cones, transforming them into mixed complementarity problems, and proposes solution methods like Newton and Levenberg-Marquardt algorithms, supported by numerical examples.

Contribution

It introduces a novel conversion of complementarity problems on extended second order cones into mixed problems and provides solution strategies with numerical validation.

Findings

Conversion of problems into mixed complementarity form

Necessary and sufficient conditions for solutions

Implementation of Newton and Levenberg-Marquardt methods

Abstract

In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg-Marquardt algorithm. Finally, we present some numerical examples.