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Title of Journal: Math Meth Oper Res

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Abbravation: Mathematical Methods of Operations Research

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Springer-Verlag

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10.1007/bf00619908

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1432-5217

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Biconvex sets and optimization with biconvex funct

Authors: Jochen Gorski Frank Pfeuffer Kathrin Klamroth
Publish Date: 2007/06/22
Volume: 66, Issue: 3, Pages: 373-407
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Abstract

The problem of optimizing a biconvex function over a given biconvex or compact set frequently occurs in theory as well as in industrial applications for example in the field of multifacility location or medical image registration Thereby a function fXtimes YtomathbbR is called biconvex if fxy is convex in y for fixed x∈X and fxy is convex in x for fixed y∈Y This paper presents a survey of existing results concerning the theory of biconvex sets and biconvex functions and gives some extensions In particular we focus on biconvex minimization problems and survey methods and algorithms for the constrained as well as for the unconstrained case Furthermore we state new theoretical results for the maximum of a biconvex function over biconvex sets

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