Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation

Sourour Elloumi (), Amélie Lambert () and Arnaud Lazare ()
Additional contact information
Sourour Elloumi: UMA-ENSTA
Amélie Lambert: CEDRIC-Cnam
Arnaud Lazare: UMA-ENSTA

Journal of Global Optimization, 2021, vol. 80, issue 2, No 1, 248 pages

Abstract: Abstract We propose a method called Polynomial Quadratic Convex Reformulation (PQCR) to solve exactly unconstrained binary polynomial problems (UBP) through quadratic convex reformulation. First, we quadratize the problem by adding new binary variables and reformulating (UBP) into a non-convex quadratic program with linear constraints (MIQP). We then consider the solution of (MIQP) with a specially-tailored quadratic convex reformulation method. In particular, this method relies, in a pre-processing step, on the resolution of a semi-definite programming problem where the link between initial and additional variables is used. We present computational results where we compare PQCR with the solvers Baron and Scip. We evaluate PQCR on instances of the image restoration problem and the low auto-correlation binary sequence problem from MINLPLib. For this last problem, 33 instances were unsolved in MINLPLib. We solve to optimality 10 of them, and for the 23 others we significantly improve the dual bounds. We also improve the best known solutions of many instances.

Keywords: Unconstrained binary polynomial programming; Global optimization; Semi-definite programming; Quadratic convex reformulation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-020-00972-2

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