Searching for and Quantifying Nonconvexity Regions of Functions*
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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.
Keywordsconvex analysis nonconvexity penalty function Hessian Weyl inequality risk assessment
MSC15B57 26B25 52A41 91G80
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