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We discuss the tropical analogues of several basic questions of convex duality.
Affine buildings and tropical convexity
M. Joswig, B. Sturmfels, and J. Yu · 1918
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Stochastic games with perfect information and time average payoff
T. M. Liggett and S. A. Lippman · 1969
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The maximum numbers of faces of a convex polytope
P. McMullen · 1970
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A general separation theorem in extremal algebras
K. Zimmermann · 1977
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Minimax Algebra
R. A. Cuninghame-Green · 1979
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Invariant half-lines of nonexpansive piecewise-linear transformations
E. Kohlberg · 1980
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An elimination method for finding all solutions of the system of linear equations over an extremal algebra
P. Butkovič and G. Hegedüs · 1984
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Cyclic games and finding minimax mean cycles in digraphs
V. A. Gurvich, A. V. Karzanov, and L. G. Khachiyan · 1988
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Synchronization and Linearity
F. Baccelli, G. Cohen, G.-J. Olsder, and J.-P. Quadrat · 1992
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Théorie des systèmes linéaires dans les dioïdes
S. Gaubert · 1992
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Convex sets in the semimodule of bounded functions
S. N. Samborskiĭ and G. B. Shpiz · 1992
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On the complexity of dualization of monotone disjunctive normal forms
M. L. Fredman and L. Khachiyan · 1996
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The complexity of mean payoff games on graphs
U. Zwick and M. Paterson · 1996
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Methods and applications of (max,+) linear algebra
S. Gaubert and M. Plus · 1997
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Numerical computation of spectral elements in max-plus algebra
J. Cochet-Terrasson, G. Cohen, S. Gaubert, M. M. Gettrick, and J. P. Quadrat · 1998
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The duality theorem for min-max functions
S. Gaubert and J. Gunawardena · 1998
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A non-linear hierarchy for discrete event dynamical systems
S. Gaubert and J. Gunawardena · 1998
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Lectures on Polytopes
G. M. Ziegler · 1998
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A constructive fixed point theorem for min-max functions
J. Cochet-Terrasson, S. Gaubert, and J. Gunawardena · 1999
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Idempotent functional analysis: an algebraic approach
G. L. Litvinov, V. P. Maslov, and G. B. Shpiz · 2001
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Dual-bounded generating problems: All minimal integer solutions for a monotone system of linear inequalities
E. Boros, K. Elbassioni, V. Gurvich, L. Khachiyan, and K. Makino · 2002
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Lectures on discrete geometry
J. Matoušek · 2002
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B \mathbb{B} -convexity
W. Briec and C. Horvath · 2004
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The Minkowski theorem for max-plus convex sets
S. Gaubert and R. D. Katz · 2007
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The max-atom problem and its relevance
M. Bezem, R. Nieuwenhuis, and E. Rodríguez-Carbonell · 2008
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A note on systems with max-min and max-product constraints
K. M. Elbassioni · 2008
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Tropical polyhedra are equivalent to mean payoff games
M. Akian, S. Gaubert, and A. Guterman · 2009
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Computing the extreme points of tropical polyhedra
X. Allamigeon, S. Gaubert, and É. Goubault · 2009
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Static analysis of memory manipulations by abstract interpretation — Algorithmics of tropical polyhedra, and application to abstract interpretation
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G. Cohen, S. Gaubert, and J. P. Quadrat · 2004
Cited alongside, same era.
Tropical convexity
M. Develin and B. Sturmfels · 2004
Cited alongside, same era.
The Perron-Frobenius theorem for homogeneous, monotone functions
S. Gaubert and J. Gunawardena · 2004
Cited alongside, same era.
Scheduling with AND/OR precedence constraints
R. H. Möhring, M. Skutella, and F. Stork · 2004
Cited alongside, same era.
Max-plus convex sets and functions
G. Cohen, S. Gaubert, J. P. Quadrat, and I. Singer · 2005
Cited alongside, same era.
Tropical halfspaces
M. Joswig · 2005
Cited alongside, same era.
X. Allamigeon · 2009
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TPLib: Tropical polyhedra library in OCaml
X. Allamigeon · 2009
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The tropical analogue of polar cones
S. Gaubert and R. D. Katz · 2009
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The level set method for the two-sided max-plus eigenproblem
S. Gaubert and S. Sergeev · 2009
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Tropical convex hull computations
M. Joswig · 2009
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The correspondence between tropical convexity and mean payoff games
M. Akian, S. Gaubert, and A. Guterman · 2010
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The tropical double description method
X. Allamigeon, S. Gaubert, and É. Goubault · 2010
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The number of extreme points of tropical polyhedra
X. Allamigeon, S. Gaubert, and R. D. Katz · 2010
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Hard problems in max-algebra, control theory, hypergraphs and other areas
M. Bezem, R. Nieuwenhuis, and E. Rodríguez-Carbonell · 2010
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Minimal half-spaces and external representation of tropical polyhedra
S. Gaubert and R. D. Katz · 2010
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Carathéodory, Helly and the others in the max-plus world
S. Gaubert and F. Meunier · 2010
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