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Algebraic solutions of tropical optimization problems

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Abstract

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 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 functions.

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  1. St. Petersburg State University, Universitetskii pr. 28, St. Petersburg, 198504, Russia

    N. Krivulin

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Krivulin, N. Algebraic solutions of tropical optimization problems. Lobachevskii J Math 36, 363–374 (2015). https://doi.org/10.1134/S199508021504006X

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  • DOI: https://doi.org/10.1134/S199508021504006X

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