Generating functions and duality for integer programs
نویسندگان
چکیده
منابع مشابه
Generating functions and duality for integer programs
We consider the integer program P→max{c′x|Ax = y;x ∈ N}. Using the generating function of an associated counting problem, and a generalized residue formula of Brion and Vergne, we explicitly relate P with its continuous linear programming (LP) analogue and provide a characterization of its optimal value. In particular, dual variables λ ∈ R have discrete analogues z ∈ C, related in a simple mann...
متن کاملErratum to "Generating functions and duality for integer programs": [Discrete Optimization 1 (2) (2004) 167-187]
Erratum Erratum to " Generating functions and duality for integer programs " ଁ In this paper, the integral sign ' ' has been used in several places, whereas the correct entry would have been 'int', the abbreviation for 'interior'.
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The theory of duality for linear programs is well-developed and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixed integer linear programs, but this has proven difficult, in part because duality theory does not integrate well with current computational practice. This paper surveys what is known...
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For an integer linear program, Gomory’s corner relaxation is obtained by ignoring the nonnegativity of the basic variables in a tableau formulation. In this paper, we do not relax these nonnegativity constraints. We generalize a classical result of Gomory and Johnson characterizing minimal cut-generating functions in terms of subadditivity, symmetry, and periodicity. Our result is based on a ne...
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ژورنال
عنوان ژورنال: Discrete Optimization
سال: 2004
ISSN: 1572-5286
DOI: 10.1016/j.disopt.2003.12.002