52 research outputs found
Algebraic solutions of tropical optimization problems
We consider multidimensional optimization problems, which are formulated and
solved in terms of tropical mathematics. The problems are to minimize
(maximize) a linear or nonlinear function defined on vectors of a
finite-dimensional semimodule over an idempotent semifield, and may have
constraints in the form of linear equations and inequalities. The aim of the
paper is twofold: first to give a broad overview of known tropical optimization
problems and solution methods, including recent results; and second, to derive
a direct, complete solution to a new constrained optimization problem as an
illustration of the algebraic approach recently proposed to solve tropical
optimization problems with nonlinear objective function.Comment: 25 pages, presented at Intern. Conf. "Algebra and Mathematical Logic:
Theory and Applications", June 2-6, 2014, Kazan, Russi
Methods of tropical optimization in rating alternatives based on pairwise comparisons
We apply methods of tropical optimization to handle problems of rating
alternatives on the basis of the log-Chebyshev approximation of pairwise
comparison matrices. We derive a direct solution in a closed form, and
investigate the obtained solution when it is not unique. Provided the
approximation problem yields a set of score vectors, rather than a unique (up
to a constant factor) one, we find those vectors in the set, which least and
most differentiate between the alternatives with the highest and lowest scores,
and thus can be representative of the entire solution.Comment: 9 pages, presented at the Annual Intern. Conf. of the German
Operations Research Society (GOR), Helmut Schmidt University Hamburg,
Germany, August 30 - September 2, 201
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