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.

本文针对具有凸二次约束的非凸二次规划提出了一种新颖的二次凸重构（QCR）。这种新的 QCR 基于同时对角化技术，该技术已成为二次规划领域中最热门的工具之一。我们首先证明可以通过解决原始问题的 Shor 松弛来实现“最佳”QCR。然后，我们设计了一种基于所提出的 QCR 的分支定界算法，以获得全局最优解。对扩展 Celis-Dennis-Tapia 问题和最优频谱共享问题的数值实验表明，我们提出的 QCR 很好地平衡了绑定质量和计算效率，因此它与两个最先进的 QCR 非常有竞争力。由相同的分支定界方案执行。