Convexity plays a prominent role in a number of areas, but practical considerations often lead to nonconvex functions. We suggest a method for determining regions of convexity and also for assessing the lack of convexity of functions in the other regions. The method relies on a specially constructed decomposition of symmetric matrices. Illustrative examples accompany theoretical results.

中文翻译：

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搜索和量化函数的非凸区域*

凸性在许多领域发挥着重要作用，但实际考虑通常会导致非凸函数。我们提出了一种确定凸性区域以及评估其他区域中函数缺乏凸性的方法。该方法依赖于对称矩阵的特殊构造分解。说明性的例子伴随着理论结果。