Some convex programs without a duality gap

Authors:
Paul Tseng
Affiliations:
University of Washington, Department of Mathematics, 98195, Seattle, WA, USA
Venue:
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Year:
2008

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Characterizing robust set containments and solutions of uncertain linear programs without qualifications

Operations Research Letters

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Abstract

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.