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arXiv · 1802.09630

Searching for, and quantifying, non-convexity of functions

Youri Davydov·Elina Moldavskaya·Ričardas Zitikis
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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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Youri Davydov, Elina Moldavskaya, Ričardas Zitikis. 2018-02-26. Searching for, and quantifying, non-convexity of functions. https://arxiv.org/abs/1802.09630

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