Linear Complementarity Problem on the Monotone Extended Second Order Cone

TL;DR

This paper investigates linear complementarity problems on monotone extended second order cones, converting them into mixed complementarity problems, and demonstrates solution methods including semi-smooth Newton, with applications to portfolio optimization.

Contribution

It introduces a novel conversion of LCPs on monotone extended second order cones into mixed complementarity problems and applies semi-smooth Newton methods for solutions.

Findings

Conversion of LCP to mixed complementarity problem.

Semi-smooth Newton method effectively solves the converted problem.

Explicit solution derived for a portfolio optimization problem.

Abstract

In this paper, we study the linear complementarity problems on the monotone extended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed complementarity problem on the non-negative orthant. We prove that any point satisfying the FB equation is a solution of the converted problem. We also show that the semi-smooth Newton method could be used to solve the converted problem, and we also provide a numerical example. Finally, we derive the explicit solution to a portfolio optimisation problem based on the monotone extended second order cone.