Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation

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.

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