An extremal property of the eigenvalue of irreducible matrices in idempotent algebra and solution of the Rawls location problem

DOI10.3103/S1063454111040078zbMath1272.15007MaRDI QIDQ357753

Nikolai Krivulin

Publication date: 13 August 2013

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

zbMATH Keywords

idempotent semifieldirreducible matrixrectilinear distanceextremal propertymatrix eigenvalue and eigenvectorRawls location problemvector semimodule

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (11)

Algebraic solutions of tropical optimization problems ⋮ On an algebraic solution of the Rawls location problem in the plane with rectilinear metric ⋮ Solution of a tropical optimization problem with linear constraints ⋮ Algebraic solution of minimax single-facility constrained location problems with Chebyshev and rectilinear distances ⋮ Tropical optimization problems with application to project scheduling with minimum makespan ⋮ Using tropical optimization to solve minimax location problems with a rectilinear metric on the line ⋮ Direct solution to constrained tropical optimization problems with application to project scheduling ⋮ Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance ⋮ Extremal properties of tropical eigenvalues and solutions to tropical optimization problems ⋮ On the rank-one approximation of positive matrices using tropical optimization methods ⋮ A multidimensional tropical optimization problem with a non-linear objective function and linear constraints

Cites Work

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• Evaluation of bounds on the mean rate of growth of the state vector of a linear dynamical stochastic system in idempotent algebra
• Minimax algebra and applications
• Disjunctive optimization, \(\max\)-separable problems and extremal algebras
• One class of separable optimization problems: solution method, application
• Max-linear Systems: Theory and Algorithms

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