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On a Frank-Wolfe type theorem in cubic optimization


Klatte, Diethard (2019). On a Frank-Wolfe type theorem in cubic optimization. Optimization, 68(2-3):539-547.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Control and Optimization
Social Sciences & Humanities > Management Science and Operations Research
Physical Sciences > Applied Mathematics
Language:English
Date:4 March 2019
Deposited On:07 Mar 2019 09:14
Last Modified:01 Aug 2020 00:00
Publisher:Taylor & Francis
ISSN:0233-1934
Additional Information:According to the Copyright Agreement the Preprint may be published in Merlin and ZORA. For the published version please contact the author.
OA Status:Green
Publisher DOI:https://doi.org/10.1080/02331934.2019.1566327
Other Identification Number:merlin-id:17552

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