SIAM Journal on Optimization, Volume 31, Issue 1, Page 142-171, January 2021.
We consider the global optimization of nonconvex (mixed-integer) quadratic programs. We present a family of convex quadratic relaxations derived by convexifying nonconvex quadratic functions through perturbations of the quadratic matrix. We investigate the theoretical properties of these relaxations and show that they are equivalent to some particular semidefinite programs. We also introduce novel branching variable selection strategies motivated by the quadratic relaxations investigated in this paper. The proposed relaxation and branching techniques are implemented in the global optimization solver BARON and tested by conducting numerical experiments on a large collection of problems. Results demonstrate that the proposed implementation leads to very significant reductions in BARON's computational times to solve the test problems.

中文翻译：

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混合整数二次程序全局优化的谱弛豫和分支策略

SIAM优化杂志，第31卷，第1期，第142-171页，2021年1月。
我们考虑非凸（混合整数）二次程序的全局优化。我们提出了通过二次矩阵的摄动使非凸二次函数凸出而得到的一系列凸二次松弛。我们研究了这些松弛的理论特性，并表明它们等效于某些特定的半定程序。我们还介绍了本文研究的二次松弛所激发的新颖分支变量选择策略。拟议的松弛和分支技术在全局优化求解器BARON中实现，并通过对大量问题进行数值实验进行了测试。结果表明，所提出的实施方案大大减少了BARON解决测试问题的计算时间。