The monotone extended second order cone and mixed complementarity problems

TL;DR

This paper introduces the Monotone Extended Second Order Cone (MESOC), explores its properties, and demonstrates its application to nonlinear and mixed complementarity problems with computational examples.

Contribution

It presents the first detailed study of MESOC, including its properties, reducibility, and its role in formulating complementarity problems.

Findings

MESOC has computable Lyapunov rank.

A cylinder is an isotonic projection set w.r.t. MESOC.

Application to complementarity problems demonstrated with an example.

Abstract

In this paper, we study a new generalization of the Lorentz cone, called the Monotone Extended Second Order Cone (MESOC). We investigate basic properties of MESOC including computation of its Lyapunov rank and proving its reducibility. Moreover, we show that in an ambient space, a cylinder is an isotonic projection set with respect to MESOC. We also examine a Nonlinear Complementarity Problem on a cylinder, which is equivalent to a suitable Mixed Complementarity Problem and provide a computational example illustrating applicability of MESOC.