

Softcover ISBN: | 978-1-4704-6741-8 |
Product Code: | GSM/219.S |
List Price: | $85.00 |
MAA Member Price: | $76.50 |
AMS Member Price: | $68.00 |
Electronic ISBN: | 978-1-4704-6740-1 |
Product Code: | GSM/219.E |
List Price: | $85.00 |
MAA Member Price: | $76.50 |
AMS Member Price: | $68.00 |
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Book DetailsGraduate Studies in MathematicsVolume: 219; 2021; 398 ppMSC: Primary 14; 52; 90;
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using \(\texttt{polymake}\).
ReadershipGraduate students and researchers interested in combinatorial, polyhedral, and optimization aspects (as opposed to algebraic geometry aspects) of tropical geometry.
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Table of Contents
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Chapters
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Tropical hypersurfaces
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Fields of power series and tropicalization
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Graph algorithms and polyhedra
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Products of tropical polynomials and the Cayley trick
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Tropical convexity
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Combinatorics of tropical polytopes
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Tropical half-spaces
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Tropical linear programming
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Feasibility and mean payoffs
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Matroids and tropical linear spaces
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Geometric combinatorics
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Computational complexity
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Using $\texttt {polymake}$
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Hints to selected problems
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Additional Material
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RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using \(\texttt{polymake}\).
Graduate students and researchers interested in combinatorial, polyhedral, and optimization aspects (as opposed to algebraic geometry aspects) of tropical geometry.
-
Chapters
-
Tropical hypersurfaces
-
Fields of power series and tropicalization
-
Graph algorithms and polyhedra
-
Products of tropical polynomials and the Cayley trick
-
Tropical convexity
-
Combinatorics of tropical polytopes
-
Tropical half-spaces
-
Tropical linear programming
-
Feasibility and mean payoffs
-
Matroids and tropical linear spaces
-
Geometric combinatorics
-
Computational complexity
-
Using $\texttt {polymake}$
-
Hints to selected problems