A simultaneous diagonalization-based quadratic convex reformulation for nonconvex quadratically constrained quadratic program

• Published in: Optimization Vol. 71; no. 9; pp. 2529 - 2545
• Main Authors: Zhou, Jing, Chen, Shenghong, Yu, Siying, Tian, Ye
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.09.2022; Taylor & Francis LLC
• Subjects: Algorithms; branch-and-bound algorithm; Constraints; Microbalances; Quadratic convex reformulation; Quadratic programming; quadratically constrained quadratic program; simultaneous diagonalization
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2020.1865347

This paper proposes a novel quadratic convex reformulation (QCR) for the nonconvex quadratic program with convex quadratic constraints. This new QCR is based on the technique of simultaneous diagonalization which has become one of the hottest tools in the area of quadratic programming. We first demonstrate that the 'best' QCR can be achieved by solving a Shor relaxation of the original problem. Then, we design a branch-and-bound algorithm based on the proposed QCR for obtaining the global optimal solution. Numerical experiments with extended Celis-Dennis-Tapia problem and optimal spectrum sharing problem are conducted to show that our proposed QCR well balances the bound quality and computing efficiency, hence it is very competitive with two state-of-the-art QCRs when they are executed by the same branch-and-bound scheme.