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We consider optimization problems that are formulated and solved in the framework of tropical mathematics.
S. Gaubert, “Resource optimization and (min,+) spectral theory,” IEEE Trans. Automat. Control
1934
Earlier work this paper cites.
Princeton University Press, 1956
S. C. Kleene, “Representation of events in nerve nets and finite automata,” in Automata Studies · 1956
Earlier work this paper cites.
R. Bellman, “On a quasi-linear equation,” Canad. J. Math
1956
Earlier work this paper cites.
S. N. N. Pandit, “A new matrix calculus,” J. SIAM
1961
Earlier work this paper cites.
R. Bellman and W. Karush, “On a new functional transform in analysis: The maximum transform,” Bull. Amer. Math. Soc
1961
Earlier work this paper cites.
R. A. Cuninghame-Green, “Describing industrial processes with interference and approximating their steady-state behaviour,” Oper. Res. Quart
1962
Earlier work this paper cites.
R. Bellman and W. Karush, “Mathematical programming and the maximum transform,” Journal of the Society for Industrial and Applied Mathematics
1962
Earlier work this paper cites.
I. V. Romanovsky, “Some remarks on the functional transformation of Bellman-Karush,” Vestnik Leningrad Univ
1962
Earlier work this paper cites.
B. Giffler, “Scheduling general production systems using schedule algebra,” Naval Res. Logist. Quart
1963
Earlier work this paper cites.
A. J. Hoffman, “On abstract dual linear programs,” Naval Res. Logist. Quart
1963
Earlier work this paper cites.
N. N. Vorob’ev, “The extremal matrix algebra,” Soviet Math. Dokl
1963
Earlier work this paper cites.
I. V. Romanovskiĭ, “Asymptotic behavior of dynamic programming processes with a continuous set of states,” Soviet Math. Dokl
1964
Earlier work this paper cites.
I. V. Romanovskii, “Asymptotic representation of recurrence relations in dynamic programming,” Soviet Phys. Dokl
1965
Earlier work this paper cites.
A. A. Korbut, “Extremal spaces,” Soviet Math. Dokl
1965
Earlier work this paper cites.
I. V. Romanovskii, “Optimization of stationary control of a discrete deterministic process,” Cybernetics
1967
Earlier work this paper cites.
N. N. Vorob’ev, “Extremal algebra of positive matrices,” Elektron. Informationsverarbeit. Kybernetik
1967
Earlier work this paper cites.
Princeton University Press, Princeton, NJ, 1970
R. T. Rockafellar, Convex Analysis · 1970
Earlier work this paper cites.
N. N. Vorob’ev, “Extremal algebra of non-negative matrices,” Elektron. Informationsverarbeit. Kybernetik
1970
Earlier work this paper cites.
I. V. Romanovskiy, “Deterministic processes of dynamic programming with additional constraints,” J. Cybernet
1972
Earlier work this paper cites.
A. A. Korbut, “Extremal vector spaces and their properties,” Elektron. Informationsverarbeit. Kybernetik
1972
Earlier work this paper cites.
G. M. Engel and H. Schneider, “Diagonal similarity and equivalence for matrices over groups with 0,” Czechoslovak Math. J
1975
Earlier work this paper cites.
R. A. Cuninghame-Green, “Projections in minimax algebra,” Math. Program
1976
Earlier work this paper cites.
PhD thesis, The City University of New York, New York, 1978
L. Superville, Various Aspects of Max-Algebra · 1978
Earlier work this paper cites.
Springer, Berlin, 1979
R. Cuninghame-Green, Minimax Algebra · 1979
Cited alongside, same era.
Oxford Applied Mathematics and Computing Science Series. Clarendon Press, Oxford, 1979
B. Carré, Graphs and Networks · 1979
Cited alongside, same era.
Elsevier, Amsterdam, 1981
U. Zimmermann, Linear and Combinatorial Optimization in Ordered Algebraic Structures · 1981
Cited alongside, same era.
Elsevier, Amsterdam, 1984
P. Butkovič, “On properties of solution sets of extremal linear programs,” in Algebraic and Combinatorial Methods in Operations Research · 1984
Cited alongside, same era.
Springer, Berlin, 1984
K. Zimmermann, “Some optimization problems with extremal operations,” in Mathematical Programming at Oberwolfach II · 1984
Cited alongside, same era.
Elsevier, Amsterdam, 1984
K. Zimmermann, “On max-separable optimization problems,” in Algebraic and Combinatorial Methods in Operations Research · 1984
Cited alongside, same era.
N. K. Krivulin, “Solution of generalized linear vector equations in idempotent algebra,” Vestnik St. Petersburg Univ. Math
2006
Later among the works it cites.
Springer, New York, 2006
K. Zimmermann, “Interval linear systems and optimization problems over max-algebras,” in Linear Optimization Problems with Inexact Data · 2006
Later among the works it cites.
G. Litvinov, “Maslov dequantization, idempotent and tropical mathematics: A brief introduction,” J. Math. Sci. (NY)
2007
Later among the works it cites.
Taylor and Francis, Boca Raton, FL, 2007
M. Akian, R. Bapat, and S. Gaubert, “Max-plus algebra,” in Handbook of Linear Algebra · 2007
Later among the works it cites.
Springer, New York, 2008
M. Gondran and M. Minoux, Graphs, Dioids and Semirings: New Models and Algorithms , vol. 41 of Operations Research / Computer Science Interfaces · 2008
Later among the works it cites.
Saint Petersburg University Press, Saint Petersburg, 2009
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R. A. Cuninghame-Green, “Minimax algebra and applications,” Fuzzy Sets and Systems
1991
Cited alongside, same era.
AMS, Providence, RI, 1992
V. P. Maslov and S. N. Samborskiĭ, vol. 13 of Advances in Soviet Mathematics · 1992
Cited alongside, same era.
K. Zimmermann, “Optimization problems with unimodal functions in max-separable constraints,” Optimization
1992
Cited alongside, same era.
Wiley Series in Probability and Statistics. Wiley, Chichester, 1993
F. L. Baccelli, G. Cohen, G. J. Olsder, and J.-P. Quadrat, Synchronization and Linearity: An Algebra for Discrete Event Systems · 1993
Cited alongside, same era.
Nauka, Moscow, 1994
V. Maslov and V. Kolokoltsov, Idempotent Analysis and Its Applications to Optimal Control Theory · 1994
Cited alongside, same era.
PhD thesis, Katholieke Universiteit Leuven, Leuven, 1996
B. De Schutter, Max-Algebraic System Theory for Discrete Event Systems · 1996
Cited alongside, same era.
N. K. Krivulin, Methods of Idempotent Algebra for Problems in Modeling and Analysis of Complex Systems · 2009
Later among the works it cites.
P. Butkovič and A. Aminu, “Introduction to max-linear programming,” IMA J. Manag. Math
2009
Later among the works it cites.
American Mathematical Society, 2009
P. Butkovič and K. P. Tam, “On some properties of the image set of a max-linear mapping,” in Tropical and Idempotent Mathematics · 2009
Later among the works it cites.
Springer Monographs in Mathematics. Springer, London, 2010
P. Butkovič, Max-linear Systems: Theory and Algorithms · 2010
Later among the works it cites.
PhD thesis, The University of Birmingham, Birmingham, 2010
K. P. Tam, Optimizing and Approximating Eigenvectors in Max-Algebra · 2010
Later among the works it cites.
L. Elsner and P. van den Driessche, “Max-algebra and pairwise comparison matrices, II,” Linear Algebra Appl
2010
Later among the works it cites.
N. K. Krivulin, “An extremal property of the eigenvalue for irreducible matrices in idempotent algebra and an algebraic solution to a Rawls location problem,” Vestnik St. Petersburg Univ. Math
2011
Later among the works it cites.
A. Aminu and P. Butkovič, “Non-linear programs with max-linear constraints: A heuristic approach,” IMA J. Manag. Math
2012
Later among the works it cites.
2012
Later among the works it cites.
M. Gavalec and K. Zimmermann, “Duality for max-separable problems,” Cent. Eur. J. Oper. Res
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
N. Krivulin, “A complete closed-form solution to a tropical extremal problem,” in Advances in Computer Science · 2012
Later among the works it cites.
B. B. Gursoy, O. Mason, and S. Sergeev, “The analytic hierarchy process, max algebra and multi-objective optimisation,” Linear Algebra Appl
2013
Later among the works it cites.
N. Krivulin and K. Zimmermann, “Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints,” in Mathematical Methods and Optimization Techniques in Engineering · 2013
Later among the works it cites.
N. Krivulin, “Explicit solution of a tropical optimization problem with application to project scheduling,” in Mathematical Methods and Optimization Techniques in Engineering · 2013
Later among the works it cites.
2013
Later among the works it cites.
N. Krivulin, “Complete solution of a constrained tropical optimization problem with application to location analysis,” in Relational and Algebraic Methods in Computer Science · 2014
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