Algebraic solutions of tropical optimization problems

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1 Scopus citations


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.
Original languageEnglish
Pages (from-to)363–374
JournalLobachevskii Journal of Mathematics
Issue number4
Early online date6 Dec 2015
StatePublished - 2015

Scopus subject areas

  • Control and Optimization
  • Algebra and Number Theory


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

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