Non-polyhedral extensions of the Frank-and-Wolfe theorem

J. E. Martinez-Legaz; D. Noll; W. Sosa

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arXiv · 1805.03451

Non-polyhedral extensions of the Frank-and-Wolfe theorem

J. E. Martinez-Legaz·D. Noll·W. Sosa

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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.

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BibTeX RIS

J. E. Martinez-Legaz, D. Noll, W. Sosa. 2018-05-09. Non-polyhedral extensions of the Frank-and-Wolfe theorem. https://arxiv.org/abs/1805.03451

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