A Comparison of Some Recent Regularity Conditions for Fenchel Duality

Part of the Springer Optimization and Its Applications book series (SOIA, volume 49)


This article provides an overview on regularity conditions for Fenchel duality in convex optimization. Our attention is focused, on the one hand, on three generalized interior-point regularity conditions expressed by means of the quasi interior and of the quasi-relative interior and, on the other hand, on two closedness-type conditions that have been recently introduced in the literature. We discuss how they do relate to each other, but also to several other classical ones and illustrate these investigations by numerous examples.


Convex optimization Fenchel duality Quasi interior Quasi-relative interior Generalized Interior-point Regularity conditions Closedness-type regularity conditions 


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The research of the first author was partially supported by DFG (German Research Foundation), project WA 922/1-3.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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