The level set method for the two-sided max-plus eigenproblem

DOI10.1007/s10626-012-0137-zzbMath1279.15024arXiv1006.5702OpenAlexW2109513024MaRDI QIDQ2393147

Stéphane Gaubert, Sergey M. Sergeev

Publication date: 7 August 2013

Published in: Discrete Event Dynamic Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.5702

zbMATH Keywords

spectrummax-plus algebrageneralized eigenproblemdiscrete event systemsmatrix pencilChebyshev distancenonlinear Perron-Frobenius theorymin-max function

Mathematics Subject Classification ID

Discrete event control/observation systems (93C65) Eigenvalues, singular values, and eigenvectors (15A18) Combinatorial games (91A46) Matrix pencils (15A22) Max-plus and related algebras (15A80)

Related Items

Weakly linear systems for matrices over the max-plus quantale, On max-plus linear dynamical system theory: the regulation problem, Tropical Fourier–Motzkin elimination, with an application to real-time verification, Analysis and control of max-plus linear discrete-event systems: an introduction, On tropical fractional linear programming, Weak dual residuations applied to tropical linear equations, Matrix representation of formal polynomials over max-plus algebra, On the continuity of the generalized spectral radius in max algebra, On the problem Ax=\lambda Bx in max algebra: every system of intervals is a spectrum, On Special Cases of the Generalized Max-Plus Eigenproblem

Cites Work

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• Tropical linear-fractional programming and parametric mean payoff games
• Tropical polar cones, hypergraph transversals, and mean payoff games
• Best approximation in max-plus semimodules
• A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
• A generalized eigenvalue problem in the max algebra
• The tropical analogue of polar cones
• Convexity and log convexity for the spectral radius
• Eigenvalues of dynamic max-min systems
• Minimax algebra
• Min-max functions
• The complexity of mean payoff games on graphs
• The equation \(A \otimes x = B \otimes y\) over \((\max,+)\)
• Max-algebra: The linear algebra of combinatorics?
• Tropical convexity
• Perturbation of eigenvalues of matrix pencils and the optimal assignment problem
• A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra
• Generalisation of the Perron-Frobenius theory to matrix pencils
• Cyclic projectors and separation theorems in idempotent convex geometry
• TROPICAL POLYHEDRA ARE EQUIVALENT TO MEAN PAYOFF GAMES
• On the problem Ax=\lambda Bx in max algebra: every system of intervals is a spectrum
• Multiorder, Kleene stars and cyclic projectors in the geometry of max cones
• Max-linear Systems: Theory and Algorithms
• Z-Pencils
• The duality theorem for min-max functions
• Asymptotics of the Perron eigenvalue and eigenvector using max-algebra
• An algorithm for exact bounds on the time separation of events in concurrent systems
• Scheduling with AND/OR Precedence Constraints
• A constructive fixed point theorem for min-max functions
• Stochastic Games with Perfect Information and Time Average Payoff
• Idempotent functional analysis: An algebraic approach