Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
A geometric Buchberger algorithm for integer programming
Mathematics of Operations Research
Variation of cost functions in integer programming
Mathematical Programming: Series A and B
Buchberger Algorithm and Integer Programming
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Non-standard approaches to integer programming
Discrete Applied Mathematics
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We consider the integer program P-max{c^'x|Ax=y;x@?N^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 @l@?R^m have discrete analogues z@?C^m, related in a simple manner. Moreover, both optimal values of P and the LP obey the same formula, using z for P and |z| for the LP. One retrieves (and refines) the so-called group-relaxations of Gomory which, in this dual approach, arise naturally from a detailed analysis of a generalized residue formula of Brion and Vergne. Finally, we also provide an explicit formulation of a dual problem P^*, the analogue of the dual LP in linear programming.