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Contribution Details

Type Journal Article
Scope Discipline-based scholarship
Title On a Frank-Wolfe type theorem in cubic optimization
Organization Unit
Authors
  • Diethard Klatte
Item Subtype Original Work
Refereed Yes
Status Published electronically before print/final form (Epub ahead of print)
Language
  • English
Journal Title Optimization
Publisher Taylor&Francis
Geographical Reach international
Page Range 1 - 9
Date 2019
Abstract Text A classical result due to Frank and Wolfe (1956) says that a quadratic function $f$ attains its supremum on a nonempty polyhedron $M$ if $f$ is bounded from above on $M$. In this note, we present a stringent proof of the extension of this result to cubic optimization (known from Andronov, Belousov and Shironin (1982)). Further, we discuss related results. In particular, we bring back to attention Kummer's (1977) generalization of the Frank-Wolfe theorem to the case that $f$ is quadratic, but $M$ is the Minkowski sum of a compact set and a polyhedral cone.
Digital Object Identifier 10.1080/02331934.2019.1566327
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