Aequationes mathematicae

, Volume 85, Issue 1–2, pp 119–130

Structural results on convexity relative to cost functions

Article

DOI: 10.1007/s00010-012-0129-y

Cite this article as:
Mitroi, FC. & Ion, D.A. Aequat. Math. (2013) 85: 119. doi:10.1007/s00010-012-0129-y
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Abstract

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 Classification

26A51 

Keywords

Cost function cost subdifferential cost convex function Jensen inequality Fenchel transform 

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CraiovaCraiovaRomania

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