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Lobachevskii Journal of Mathematics

, Volume 36, Issue 4, pp 363–374 | Cite as

Algebraic solutions of tropical optimization problems

  • N. Krivulin
Article

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.

Keywords and phrases

Idempotent semifield tropical optimization problem nonlinear objective function linear inequality constraint direct solution 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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