Non polyhedral convex envelopes for 1-convex functions

Marco Locatelli ()
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Marco Locatelli: Università di Parma

Journal of Global Optimization, 2016, vol. 65, issue 4, No 1, 637-655

Abstract: Abstract In this paper we discuss how to derive the non polyhedral convex envelopes for some functions, called 1-convex throughout the paper, over boxes. The main result is about n-dimensional 1-convex functions, but we get to it by first discussing in detail some special cases, namely functions $$xyz^\delta $$ x y z δ , $$\delta >1$$ δ > 1 , and, next, more general trivariate functions. The relation between the class of functions investigated in this paper and other classes investigated in the existing literature is discussed.

Keywords: Non polyhedral convex envelopes; Trivariate functions; 1-Convex functions (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10898-016-0409-5

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