Theory of linear and integer programming
Theory of linear and integer programming
Modern computer algebra
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions
SIAM Journal on Optimization
A O(1/ε2)n-time sieving algorithm for approximate integer programming
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We study a particular case of integer polynomial optimization: Minimize a polynomial F@^ on the set of integer points described by an inequality system F"1==2 is an upper bound for the total degree of the polynomials involved and l denotes the maximum binary length of all coefficients. The algorithm is polynomial for a fixed number n of variables and represents a direct generalization of Lenstra's algorithm [Math. Oper. Res. 8 (1983) 538-548] in integer linear optimization. In the considered case, our complexity-result improves the algorithm given by Khachiyan and Porkolab [Discrete Comput. Geom. 23 (2000) 207-224] for integer optimization on convex semialgebraic sets.