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 ω-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.

► Improvement of previous methods to compute the ω-invariant of a numerical semigroup. ► New application of optimizing a linear function over an efficient integer. ► Efficiency of optimization techniques for solving problems in abstract algebra. ► Bidirectional collaborations between two different areas: algebra and OR. ► Use of algebraic properties to translate problems to discrete optimization problems.