An extension of an RLT-based solver to MINLP polynomial problems

TL;DR

This paper extends the RAPOSa solver's branch-and-bound algorithm to handle mixed-integer polynomial problems by replacing LP relaxations with MILP ones, improving bounds for mixed-integer polynomial optimization.

Contribution

It introduces a direct adaptation of an RLT-based solver to mixed-integer problems, analyzing key choices for effective bounds.

Findings

Effective handling of mixed-integer polynomial problems.

Analysis of algorithmic choices impacts bounds quality.

Extension maintains efficiency of the original solver.

Abstract

In this paper we extend the core branch-and-bound algorithm of an RLT-based solver for continuous polynomial optimization, RAPOSa, to handle mixed-integer problems. We do so by a direct adaptation, in which LP relaxations are replaced with MILP ones and, therefore, the additional burden caused by the discrete variables is taken care of by the auxiliary MILP solver. The analysis then focuses on the impact of a number of choices that must be made for the resulting algorithm to be effective at providing good lower and upper bounds upon termination.