Abstract
Given a general primal problem and its Fenchel–Lagrange dual one, which is obtained by using a conjugation scheme based on coupling functions and the perturbational approach, the aim in this work is to establish conditions under which strong duality can be guaranteed. To this purpose, even convexity and properness are a compulsory requirement over the involved functions in the primal problem. Furthermore, two closedness-type regularity conditions and a characterization for strong duality are derived.
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Acknowledgements
This research was partially supported by MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P and by Consellería de Educación de la Generalitat Valenciana, Spain, Pre-doc Program Vali+d, DOCV 6791/07.06.2012, Grant ACIF-2013-156. The authors wish to thank anonymous referee for her/his valuable comments and suggestions that have significantly improved the quality of the paper.
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Vaithilingam Jeyakumar.
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Fajardo, M.D., Vidal, J. Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme. J Optim Theory Appl 176, 57–73 (2018). https://doi.org/10.1007/s10957-017-1209-x
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DOI: https://doi.org/10.1007/s10957-017-1209-x
Keywords
- Evenly convex function
- Generalized convex conjugation
- Fenchel–Lagrange dual problem
- Regularity condition