A mathematical programming approach to the computation of the omega invariant of a numerical semigroup
In this paper we present a mathematical programming formulation for the [omega]-invariant of a numerical semigroup for each of its minimal generators which is an useful index in commutative algebra (in particular in factorization theory) to analyze the primality of the elements in the semigroup. The model consists of solving a problem of optimizing a linear function over the efficient set of a multiobjective linear integer program. We offer a methodology to solve this problem and we provide some computational experiments to show the efficiency of the proposed algorithm.
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- Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.
- Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.
- Özlen, Melih & Azizoglu, Meral, 2009. "Multi-objective integer programming: A general approach for generating all non-dominated solutions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 25-35, November.
- Abbas, Moncef & Chaabane, Djamal, 2006. "Optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1140-1161, October.
- Odile Marcotte & Richard M. Soland, 1986. "An Interactive Branch-and-Bound Algorithm for Multiple Criteria Optimization," Management Science, INFORMS, vol. 32(1), pages 61-75, January.
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