TL;DR
This survey reviews the evolution of tropical convexity, highlighting its historical roots, connections to optimization, and its influence on the development of tropical geometry since the seminal 2004 paper.
Contribution
It provides a comprehensive overview of tropical convexity's development and its impact on tropical geometry, emphasizing historical context and foundational contributions.
Findings
Tropical convexity has deep roots in optimization and combinatorics.
The 2004 paper by Develin and Sturmfels significantly shaped the field.
Tropical geometry has evolved considerably since its inception.
Abstract
The term "tropical convexity" was coined by Develin and Sturmfels who published a landmark paper with that title in 2004. However, the topic has much older roots and is deeply connected to linear and combinatorial optimization and other areas of mathematics. The purpose of this survey is to sketch how that article contributed to shaping the field of tropical geometry as we know it today.
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Taxonomy
TopicsEconomic Theory and Policy