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Searching for, and quantifying, non-convexity of functions (1802.09630v2)
Published 26 Feb 2018 in math.FA and math.OC
Abstract: Convexity plays a prominent role in a number of problems, but practical considerations frequently give rise to non-convex functions. We suggest a method for determining convex regions, and also for assessing the lack of convexity in the other regions. The method relies on a specially constructed decomposition of symmetric matrices, such as the Hessian. We illustrate theoretical results using several examples, one of which analyses a problem arising in risk measurement and management in insurance and finance.
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