Mathematical Programming

, Volume 116, Issue 1, pp 553-578

Some convex programs without a duality gap

  • Paul TsengAffiliated withDepartment of Mathematics, University of Washington Email author 

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An important issue in convex programming concerns duality gap. Various conditions have been developed over the years that guarantee no duality gap, including one developed by Rockafellar (Network flows and monotropic programming. Wiley-Interscience, New York, 1984)involving separable objective function and affine constraints. We show that this sufficient condition can be further relaxed to allow the constraint functions to be separable. We also refine a sufficient condition involving weakly analytic functions by allowing them to be extended-real-valued.


Separable convex program Recession direction Duality gap Hoffman’s error bound Weakly analytic function

Mathematics Subject Classification (2000)

90C25 90C46