Linear Complementarity Problem on the Monotone Extended Second Order Cone
Optimization and Control
2025-09-03 v2
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.
Cite
@article{arxiv.2209.04386,
title = {Linear Complementarity Problem on the Monotone Extended Second Order Cone},
author = {Yingchao Gao and Sándor Z. Németh and Guohan Zhang},
journal= {arXiv preprint arXiv:2209.04386},
year = {2025}
}
Comments
Mistakes found in previous version