Non-polyhedral Extensions of the Frank and Wolfe Theorem

Juan Enrique Martinez-Legaz, Dominikus Noll () and Wilfredo Sosa ()
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Dominikus Noll: Institut de Mathématiques, Université de Toulouse
Wilfredo Sosa: Universidade Católica de Brasília, Programa de Pôs-Graduação em Economia

Chapter Chapter 12 in Splitting Algorithms, Modern Operator Theory, and Applications, 2019, pp 309-329 from Springer

Abstract: 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.

Keywords: Quadratic optimization; Asymptotes; Motzkin-sets; Frank-and-Wolfe theorem; 49M20; 65K10; 90C30 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-25939-6_12

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DOI: 10.1007/978-3-030-25939-6_12

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