# The monotone extended second order cone and mixed complementarity problems

arXiv: https://arxiv.org/abs/2103.04830 · HTML: https://mlsanity.com/paper/2103.04830/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [An introduction to optimization under uncertainty -- A short survey](https://mlsanity.com/paper/2212.00862/) (2022)

## Abstract (arXiv)

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.