A General Nonconvex Multiduality Principle

Francesca Bonenti (), Juan Enrique Martinez-Legaz and Rossana Riccardi ()
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Francesca Bonenti: Open Capital Partners SGR
Rossana Riccardi: Università degli Studi di Brescia

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 3, No 1, 527-540

Abstract: 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.

Keywords: Nonconvex optimization; Multiduality; Toland–Singer duality; 90C26; 49M29 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1245-1

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