[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.
Disciplines :
Mathematics Quantitative methods in economics & management
Author, co-author :
Crama, Yves ; Université de Liège - ULiège > HEC Liège : UER > Recherche opérationnelle et gestion de la production
Language :
English
Title :
Concave extensions for nonlinear 0-1 maximization problems
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