Some cut-generating functions for second-order conic sets

TL;DR

This paper develops new cut-generating functions for second-order conic sets, enabling more effective computation of integer hulls for conic integer programs, especially in bounded and two-dimensional cases.

Contribution

It introduces a novel class of non-decreasing cut generating functions for second-order cones and demonstrates their effectiveness in deriving integer hulls for specific conic sets.

Findings

Cut generating functions for bounded conic sets can be adapted for integer hulls.

New non-decreasing functions are sufficient for conic intersections in 2D.

Methods extend integer programming techniques to conic optimization.

Abstract

In this paper, we study cut generating functions for conic sets. Our first main result shows that if the conic set is bounded, then cut generating functions for integer linear programs can easily be adapted to give the integer hull of the conic integer program. Then we introduce a new class of cut generating functions which are non-decreasing with respect to second-order cone. We show that, under some minor technical conditions, these functions together with integer linear programming-based functions are sufficient to yield the integer hull of intersections of conic sections in $\mathbb{R}^2$.