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Excerpt from Extreme Varieties, Concave Functions, and the Fixed Charge Problem
This paper deals with various structural properties of convex sets and their application to the study of concave mappings. The investigation was prompted by a programming problem (the fixed charge problem) which involves the minimization of a concave function on a convex polyhedron. In the fixed charge problem it is not difficult to show (by an argument involving the form of the function and the polyhedral character of the domain) that the desired infimum is actually attained Oh the other hand it is not generally true that a concave function on a convex set attains its infimum, and it is natural to seek conditions under which this is so. The search for such conditions leads to the study of representations of convex sets similar to the Krein Milman theorem.
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Extreme Varieties, Concave Functions, and the Fixed Charge Problem
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Paperback. Zustand: New. Print on Demand. This book delves into the fascinating world of convex sets, concave functions, and their applications, particularly in the context of minimizing functions. The author's exploration of extreme varieties within convex sets leads to a unique decomposition theorem, providing a deeper understanding of the structure of such sets. This decomposition serves as a key tool in establishing conditions for when a concave function assumes its infimum. The book culminates by demonstrating that the fixed charge problem, a common challenge in programming, has a solution that can be found at an extreme point, expanding our knowledge of optimization techniques. Its insights into the structure and properties of convex sets and concave functions make this book an invaluable resource for mathematicians and practitioners seeking to optimize functions and solve complex programming problems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781334014918_0
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