Structural results on convexity relative to cost functions
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Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the theoretical and the computational viewpoints. We drew a parallel to the classical theory of convex functions by investigating the cost convexity and its connections with the usual convexity. We give a generalization of Jensen’s inequality for c-convex functions.
Mathematics Subject Classification26A51
KeywordsCost function cost subdifferential cost convex function Jensen inequality Fenchel transform
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