A General Nonconvex Multiduality Principle

Francesca Bonenti, Juan Enrique Martínez-Legaz, Rossana Riccardi

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. 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.
Original languageEnglish
Pages (from-to)527-540
JournalJournal of Optimization Theory and Applications
Volume176
Issue number3
DOIs
Publication statusPublished - 1 Mar 2018

Keywords

  • Multiduality
  • Nonconvex optimization
  • Toland–Singer duality

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