# Enhancing Quadratic Programming Solvers via Quadratic Nonconvex Reformulation

## TL;DR

This paper introduces a quadratic nonconvex reformulation (QNR) framework that significantly enhances the efficiency of modern quadratic programming solvers like Gurobi and SCIP, especially on challenging nonconvex problems.

## Contribution

The paper presents the first exploration of quadratic nonconvex reformulation (QNR) to improve solver performance for nonconvex quadratic programming problems.

## Key findings

- QNR substantially accelerates Gurobi and SCIP.
- Gurobi achieves state-of-the-art results with QNR on benchmarks.
- QNR is effective across diverse problem instances.

## Abstract

In this paper, we consider solving nonconvex quadratic programming problems using modern solvers such as Gurobi and SCIP. It is well-known that the classical techniques of quadratic convex reformulation can improve the computational efficiency of global solvers for mixed-integer quadratic optimization problems. In contrast, the use of quadratic nonconvex reformulation (QNR) has not been previously explored. This paper introduces a QNR framework--an unconventional yet highly effective approach for improving the performance of state-of-the-art quadratic programming solvers such as Gurobi and SCIP. Our computational experiments on diverse nonconvex quadratic programming problem instances demonstrate that QNR can substantially accelerate both Gurobi and SCIP. Notably, with QNR, Gurobi achieves state-of-the-art performance on several benchmark and randomly generated instances.