A General Nonconvex Multiduality Principle |
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Authors: | Francesca Bonenti Juan Enrique Martínez-Legaz Rossana Riccardi |
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Institution: | 1.Open Capital Partners SGR,Milan,Italy;2.Departament d’Economia i d’Història Econòmica,Universitat Autònoma de Barcelona,Barcelona,Spain;3.BGSMath,Barcelona,Spain;4.Dipartimento di Economia e Management,Università degli Studi di Brescia,Brescia,Italy |
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Abstract: | We introduce a (possibly infinite) collection of mutually dual nonconvex optimization problems, which share a common optimal value, and give a characterization of their global optimal solutions. As immediate consequences of our general multiduality principle, we obtain Toland–Singer duality theorem as well as an analogous result involving generalized perspective functions. Based on our duality theory, we propose an extension of an existing algorithm for the minimization of d.c. functions, which exploits Toland–Singer duality, to a more general class of nonconvex optimization problems. |
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