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A General Nonconvex Multiduality Principle

Author

Listed:
  • Francesca Bonenti

    (Open Capital Partners SGR)

  • Juan Enrique Martínez-Legaz

    (Universitat Autònoma de Barcelona
    BGSMath)

  • Rossana Riccardi

    (Università degli Studi di Brescia)

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.

Suggested Citation

  • Francesca Bonenti & Juan Enrique Martínez-Legaz & Rossana Riccardi, 2018. "A General Nonconvex Multiduality Principle," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 527-540, March.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:3:d:10.1007_s10957-018-1245-1
    DOI: 10.1007/s10957-018-1245-1
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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