Facial structure of copositive and completely positive cones over a second-order cone

TL;DR

This paper classifies the facial structure of copositive and completely positive cones over a second-order cone, analyzing their dimensions, exposedness, and face chains to deepen understanding of their geometric properties.

Contribution

It provides a detailed classification of faces and properties of these cones, extending the understanding of their geometric and algebraic structure.

Findings

Classified faces of the cones and analyzed their properties.

Computed parameters related to face chains of the cones.

Discussed potential extensions to general cones.

Abstract

We classify the faces of copositive and completely positive cones over a second-order cone and investigate their dimension and exposedness properties. Then we compute two parameters related to chains of faces of both cones. At the end, we discuss some possible extensions of the results with a view toward analyzing the facial structure of general copositive and completely positive cones.