Compact Linearization for Binary Quadratic Problems subject to Linear Equations

TL;DR

This paper generalizes the compact linearization method for binary quadratic problems to include arbitrary linear equations with positive coefficients, improving relaxation strength and broadening applicability.

Contribution

It extends the compact linearization technique from assignment constraints to general linear equations with positive coefficients, enhancing its utility.

Findings

The generalized linearization is as effective as traditional methods in key cases.

The approach applies to various quadratic combinatorial optimization problems.

The resulting relaxations are provably as strong as standard linearizations.

Abstract

In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients which considerably enlarges its applicability. We discuss special cases of prominent quadratic combinatorial optimization problems where the obtained compact linearization yields a continuous relaxation that is provably as least as strong as the one obtained with an ordinary linearization.