Biconvex sets and optimization with biconvex functions: a survey and extensions

Jochen Gorski (), Frank Pfeuffer () and Kathrin Klamroth ()

Mathematical Methods of Operations Research, 2007, vol. 66, issue 3, 373-407

Abstract: The problem of optimizing a biconvex function over a given (bi)convex 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 $$f:X\times Y\to{\mathbb{R}}$$ is called biconvex, if f(x,y) is convex in y for fixed x∈X, and f(x,y) 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. Copyright Springer-Verlag 2007

Keywords: Biconvex functions; Biconvex sets; Biconvex optimization; Biconcave optimization; Non-convex optimization; Generalized convexity (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (36)

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DOI: 10.1007/s00186-007-0161-1

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