Positive operators of Extended Lorentz cones

TL;DR

This paper characterizes the conditions under which linear operators are positive with respect to Extended Lorentz cones, comparing these with the classical Lorentz cone case to deepen understanding of their properties.

Contribution

It provides necessary and sufficient conditions for positive operators of Extended Lorentz cones, expanding the theoretical framework beyond traditional Lorentz cones.

Findings

Identifies conditions for positivity of linear operators on Extended Lorentz cones

Highlights differences and similarities with Lorentz cone positive operators

Enhances theoretical understanding of cone-based operator positivity

Abstract

In this paper necessary conditions and sufficient conditions are given for a linear operator to be a positive operators of an Extended Lorentz cone. Similarities and differences with the positive operators of Lorentz cones are investigated.