Abstract In this paper, we consider the nonconvex quadratic optimization problem with a single quadratic constraint. First we give a theoretical characterization of the local non-global minimizers. Then we extend the recent characterization of the global minimizer via a generalized eigenvalue problem to the local non-global minimizers. Finally, we use these results to derive an efficient algorithm that finds the global minimizer of the problem with an additional linear inequality constraint.

中文翻译：

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单二次约束二次优化问题的局部非全局极小化

摘要 在本文中，我们考虑具有单个二次约束的非凸二次优化问题。首先，我们给出局部非全局最小化器的理论表征。然后我们通过广义特征值问题将全局最小器的最新特征扩展到局部非全局最小器。最后，我们使用这些结果推导出一种有效的算法，该算法可以找到具有附加线性不等式约束的问题的全局最小值。