A comparison of alternative c-conjugate dual problems in infinite convex optimization. (4th May 2017)

• Record Type: Journal Article
• Authors: Fajardo, M. D.; Vidal, J.
• Is Part Of: Optimization. Volume 66:Number 5(2017)
• Page Start: 705
• Page End: 722
• Publication Date: 2017-05-04
• Subjects: Evenly convex function -- generalized convex conjugation -- Fenchel -- Lagrange and Fenchel–Lagrange dual problems; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1295046
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this work, we obtain a Fenchel–Lagrange dual problem for an infinite dimensional optimization primal one, via perturbational approach and using a conjugation scheme called c-conjugation instead of classical Fenchel conjugation. This scheme is based on the generalized convex conjugation theory. We analyse some inequalities between the optimal values of Fenchel, Lagrange and Fenchel–Lagrange dual problems and we establish sufficient conditions under which they are equal. Examples where such inequalities are strictly fulfilled are provided. Finally, we study the relations between the optimal solutions and the solvability of the three mentioned dual problems.