On the duality gap and Gale's example in conic linear programming

TL;DR

This paper examines duality gaps in conic linear programming, specifically addressing an open problem related to Gale's example, and revisits foundational duality results in the field.

Contribution

It provides new insights into the duality gap function for Gale's example and clarifies duality properties in conic linear programming.

Findings

Resolved an open problem regarding the duality gap in Gale's example.

Revisited and clarified duality results in conic linear programming.

Enhanced understanding of duality gaps in conic optimization.

Abstract

The aim of this paper is to revisit some duality results in conic linear programming and to answer an open problem related to the duality gap function for Gale's example.