Solution of a tropical optimization problem with linear constraints

N.K. Krivulin, V.N. Sorokin

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2 Scopus citations

Abstract

An optimization problem is considered that is formulated in terms of tropical (idempotent) mathematics and consists in the minimization of a nonlinear function in the presence of linear constraints on the domain of admissible values. The objective function is defined on the set of vectors over an idempotent semifield by a matrix with the use of the operation of multiplicative conjugate transposition. The problem considered is a further generalization of several known problems in which the solution involves the calculation of the spectral radius of the matrix. This generalization implies the use of a more complicated objective function compared with that in the above mentioned problems, and the imposition of additional constraints. To solve the new problem, an auxiliary variable is introduced that describes the minimum value of the objective function. Then the problem reduces to solving an inequality in which the auxiliary variable plays the role of a parameter. Necessary and sufficient conditions for the exis
Original languageEnglish
Pages (from-to)224-232
JournalVestnik St. Petersburg University: Mathematics
Volume48
Issue number4
DOIs
StatePublished - 2015

Keywords

  • tropical mathematics
  • idempotent semifield
  • spectral radius
  • linear inequality
  • optimization problem
  • complete solution

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