Structural results on convexity relative to cost functions
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- Mitroi, FC. & Ion, D.A. Aequat. Math. (2013) 85: 119. doi:10.1007/s00010-012-0129-y
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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.