Reference : Concave extensions for nonlinear 0-1 maximization problems
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/2268/217335
Concave extensions for nonlinear 0-1 maximization problems
English
Crama, Yves mailto [Université de Liège - ULiège > HEC Liège : UER > Recherche opérationnelle et gestion de la production >]
1993
Mathematical Programming
Springer
61
53-60
Yes (verified by ORBi)
International
0025-5610
1436-4646
[en] Nonlinear 0-1 optimization ; concave extension ; concave envelope ; linearization ; balanced matrices
[en] A well-known linearization technique for nonlinear 0-1 maximization problems can be viewed as
extending any polynomial in 0-1 variables to a concave function defined on [0, 1]. Some properties of this "standard" concave extension are investigated. Polynomials for which the standard extension coincides with the concave envelope are characterized in terms of integrality of a certain polyhedron or balancedness of a certain matrix. The standard extension is proved to be identical to another type of concave extension, defined as the lower envelope of a class of affine functions majorizing the given polynomial.
Researchers
http://hdl.handle.net/2268/217335
10.1007/BF01582138

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