TL;DR
This paper provides an overview of the historical development, fundamental concepts, and current trends in convexity theory, highlighting its foundational role in various mathematical and optimization contexts.
Contribution
It offers a comprehensive historical and conceptual overview of convexity, emphasizing its origins, evolution, and significance in mathematical analysis and optimization.
Findings
Historical insights into convexity's development
Connections between convexity and duality, optimality, and stability
Trends and future directions in convexity research
Abstract
The idea of convexity feeds generation, separation, calculus, and approximation. Generation appears as duality; separation, as optimality; calculus, as representation; and approximation, as stability. This is an overview of the origin, evolution, and trends of convexity. Study of convexity in the Sobolev Institute was initiated by Leonid Kantorovich (1912--1986) and Alexandr Alexandrov (1912--1999). This talk is a part of their memory.
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Taxonomy
TopicsAnalytic Number Theory Research · History and Theory of Mathematics · Mathematical Approximation and Integration