Mathematics – Optimization and Control
Scientific paper
2009-02-08
Journal of Symbolic Computation 2011
Mathematics
Optimization and Control
13 pages
Scientific paper
10.1016/j.jsc.2010.10.003
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been deeply studied due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem in the problem of solving one or more systems of polynomial equations and we use certain Gr\"obner bases to solve these systems. Different transformations give different methodologies that are analyzed and compared from a theoretical point of view and by some computational experiments via the algorithms that they induce.
Blanco Víctor
Puerto Justo
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