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Non-polyhedral Extensions of the Frank and Wolfe Theorem

In: Splitting Algorithms, Modern Operator Theory, and Applications

Author

Listed:
  • Juan Enrique Martínez-Legaz

    (Universitat Autònoma de Barcelona, and Barcelona Graduate School of Mathematics (BGSMath), Departament d’Economia i d’Història Econòmica)

  • Dominikus Noll

    (Institut de Mathématiques, Université de Toulouse)

  • Wilfredo Sosa

    (Universidade Católica de Brasília, Programa de Pôs-Graduação em Economia)

Abstract

In 1956 Marguerite Frank and Paul Wolfe proved that a quadratic function which is bounded below on a polyhedron P attains its infimum on P. In this work we search for larger classes of sets F with this Frank-and-Wolfe property. We establish the existence of non-polyhedral Frank-and-Wolfe sets, obtain internal characterizations by way of asymptotic properties, and investigate stability of the Frank-and-Wolfe class under various operations.

Suggested Citation

  • Juan Enrique Martínez-Legaz & Dominikus Noll & Wilfredo Sosa, 2019. "Non-polyhedral Extensions of the Frank and Wolfe Theorem," Springer Books, in: Heinz H. Bauschke & Regina S. Burachik & D. Russell Luke (ed.), Splitting Algorithms, Modern Operator Theory, and Applications, chapter 0, pages 309-329, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-25939-6_12
    DOI: 10.1007/978-3-030-25939-6_12
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