Discrete Convex Analysis

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SIAM, 2003 - Mathematics - 389 pages
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Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis. Discrete Convex Analysis provides the information that professionals in optimization will need to "catch up" with this new theoretical development. It also presents an unexpected connection between matroid theory and mathematical economics and expounds a deeper connection between matrices and matroids than most standard textbooks.
  

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Contents

Convex Functions with Combinatorial Structures
39
Convex Analysis Linear Programming and Integrality
77
Conjugacy and Duality
205
Network Flows
245
Algorithms
281
Application to Mathematical Economics
323
Application to Systems Analysis by Mixed Matrices
347
Bibliography
363
Index
379
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Page 375 - DD Siljak, Large-Scale Dynamic Systems: Stability and Structure (North-Holland, New York, 1978).

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About the author (2003)

Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology, at the University of Tokyo.

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