Softcover ISBN:  9781470467418 
Product Code:  GSM/219.S 
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eBook ISBN:  9781470467401 
EPUB ISBN:  9781470472344 
Product Code:  GSM/219.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470467418 
eBook: ISBN:  9781470467401 
Product Code:  GSM/219.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 
Softcover ISBN:  9781470467418 
Product Code:  GSM/219.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470467401 
EPUB ISBN:  9781470472344 
Product Code:  GSM/219.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470467418 
eBook ISBN:  9781470467401 
Product Code:  GSM/219.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 

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 selfcontained 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.

Table of Contents

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 halfspaces

Tropical linear programming

Feasibility and mean payoffs

Matroids and tropical linear spaces

Geometric combinatorics

Computational complexity

Using $\texttt {polymake}$

Hints to selected problems


Additional Material

Reviews

The expository style is remarkably friendly to newcomers, while the content includes several topics that a practitioner of tropical geometry may find new or refreshing. No knowledge of algebraic geometry is required throughout the textbook. An exposure to polyhedral geometry and computational complexity is helpful, for which Appendices A and B provide a suitable introduction. Each chapter includes numerous exercises and some open problems for future research, along with Appendix D which discusses them further. The textbook will become an indispensable reference for the interaction between tropical geometry and optimization.
Christopher Eur (Harvard Department of Mathematics), MathSciNet


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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 selfcontained 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 halfspaces

Tropical linear programming

Feasibility and mean payoffs

Matroids and tropical linear spaces

Geometric combinatorics

Computational complexity

Using $\texttt {polymake}$

Hints to selected problems

The expository style is remarkably friendly to newcomers, while the content includes several topics that a practitioner of tropical geometry may find new or refreshing. No knowledge of algebraic geometry is required throughout the textbook. An exposure to polyhedral geometry and computational complexity is helpful, for which Appendices A and B provide a suitable introduction. Each chapter includes numerous exercises and some open problems for future research, along with Appendix D which discusses them further. The textbook will become an indispensable reference for the interaction between tropical geometry and optimization.
Christopher Eur (Harvard Department of Mathematics), MathSciNet