Title: Essentials of tropical combinatorics /
Authors: Joswig, Michael, 1965-
Year: 2021
Subjects: Tropical geometry; Combinatorial geometry; Linear programming; Combinatorial geometry; Linear programming; Tropical geometry; Algebraic geometry -- Tropical geometry -- Combinatorial aspects of tropical varieties.; Algebraic geometry -- Tropical geometry -- Applications of tropical geometry.; Convex and discrete geometry -- Polytopes and polyhedra -- Computational aspects related to convexity.; Operations research, mathematical programming -- Mathematical programming -- Linear programming.; Operations research, mathematical programming -- Mathematical programming -- Tropical optimization (e.g., max-plus optimization).
Abstract: "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."--Back cover.
Contents: Tropical hypersturfaces -- 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.