Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme
- 191 Downloads
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.
KeywordsEvenly convex function Generalized convex conjugation Fenchel–Lagrange dual problem Regularity condition
Mathematics Subject Classification52A20 26B25 90C25
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.
- 1.Rockafellar, R.T.: Conjugate duality and optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA. (1974). Lectures given at the Johns Hopkins University, Baltimore, MD, June, 1973Google Scholar
- 3.Fenchel, W.: A remark on convex sets and polarity (Tome Supplémentaire), 82–89 (1952)Google Scholar
- 10.Wanka, G., Boţ, R.I.: On the relations between different dual problems in convex mathematical programming. In: Operations Research Proceedings, 2001 (Duisburg), pp. 255–262. Springer, Berlin (2002)Google Scholar