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On jet-convex functions and their tensor products

Vladimir Shikhman and Oliver Stein

Abstract. In this paper we introduce necessary and sufficient conditions for the tensor product of two convex functions
to be convex. For our analysis we introduce the notions of true convexity, jet-convexity, true jet-convexity
as well as true log-convexity. The links between jet-convex and log-convex functions are elaborated.
As an algebraic tool we introduce the jet product of two symmetric matrices and study some of its properties.

We illustrate our results by an application from global optimization, where a convex underestimator for the
tensor product of two functions is constructed as the tensor product of convex underestimators of the single
functions.

 

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