منابع مشابه
Sufficiency of cut-generating functions
This note settles an open problem about cut-generating functions, a concept that has its origin in the work of Gomory and Johnson from the 1970’s and has received renewed attention in recent years.
متن کاملCut-Generating Functions
In optimization problems such as integer programs or their relaxations, one encounters feasible regions of the form {x ∈ R+ : Rx ∈ S} where R is a general real matrix and S ⊂ R is a specific closed set with 0 / ∈ S. For example, in a relaxation of integer programs introduced in [ALWW2007], S is of the form Z − b where b 6∈ Z . One would like to generate valid inequalities that cut off the infea...
متن کاملOn composition of generating functions
In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...
متن کاملA geometric approach to cut-generating functions
The cutting-plane approach to integer programming was initiated more that 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. This line of research was left dormant for several decades until relatively recently, when a paper of Andersen, Louveaux, Weismantel and Wolsey gene...
متن کاملCut-Generating Functions and S-Free Sets
We consider the separation problem for sets X that are inverse images of a given set S by a linear mapping. Classical examples occur in integer programming, complementarity problems and other optimization problems. One would like to generate valid inequalities that cut off some point not lying in X , without reference to the linear mapping. Formulas for such inequalities can be obtained through...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2014
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-014-0780-2