A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone

TL;DR

This paper introduces a semi-smooth Newton method for solving projection equations and linear second order cone complementarity problems, demonstrating global convergence and practical effectiveness through computational experiments.

Contribution

It develops a semi-smooth Newton approach for second order cone problems, establishing convergence results and applying them to specific complementarity problems with positive definite matrices.

Findings

Method is well-defined under mild assumptions.

Sequence converges globally and Q-linearly.

Computational experiments confirm practical viability.

Abstract

In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is globally and Q-linearly convergent to a solution. As an application, the obtained results are used to study the linear second order cone complementarity problem, with special emphasis on the particular case of positive definite matrices. Moreover, some computational experiments designed to investigate the practical viability of the method are presented.