Network Flows and Monotropic Optimization

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Athena Scientific, Jun 1, 1999 - Mathematics - 634 pages
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A rigorous and comprehensive treatment of network flow theory and monotropic optimization by one of the world's most renowned applied mathematicians.

This classic textbook covers extensively the duality theory and the algorithms of linear and nonlinear network optimization optimization, and their significant extensions to monotropic programming (separable convex constrained optimization problems, including linear programs). It complements our other book on the subject of network optimization Network Optimization: Continuous and Discrete Models (Athena Scientific, 1998).

Monotropic programming problems are characterized by a rich interplay between combinatorial structure and convexity properties. Rockafellar develops, for the first time, algorithms and a remarkably complete duality theory for these problems.

Among its special features the book:

(a) Treats in-depth the duality theory for linear and nonlinear network optimization

(b) Uses a rigorous step-by-step approach to develop the principal network optimization algorithms

(c) Covers the main algorithms for specialized network problems, such as max-flow, feasibility, assignment, and shortest path

(d) Develops in detail the theory of monotropic programming, based on the author's highly acclaimed research

(e) Contains many examples, illustrations, and exercises

(f) Contains much new material not found in any other textbook


 

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Contents

Networks
1
Paths and Cuts
26
Flows and Capacities
53
Analysis of Flows
100
Matching Theory and Assignment Problems
137
Potentials and Spans
173
Networks with Linear Costs
235
Optimal Flows and Potentials
312
Algorithms for Convex Costs
388
Linear Systems of Variables
448
Monotropic Programming
517
Bibliography
602
Index
611
Copyright

Other editions - View all

Network Flows and Monotropic Optimization
R. T. Rockafellar
Snippet view - 1984

Common terms and phrases

applied arcs assignment associated basis c+(j capacity Chapter circuit circulation closed column compatible condition connected constraints constructed convex corresponding cost course d+(j defined described determined direction distribution algorithm dº(j dual duality elementary elements equivalent Example Exercise existence expressed extreme fact feasible distribution feasible solution Figure finite flux formula function given initial integral intervals iteration latter least matrix max flow maximal method minimize node Note obtained optimal differential problem optimal distribution problem optimal solution out-of-kilter painted pair particular path piecewise linear pivoting positive possible potential primal procedure proof Prove reduces relation relative replaced representation represented respect routing satisfying sense sequence Show simplex simplex method solving span subroutine Suppose tableau tension terminate theorem theorem in Section theory tree Tucker values vector whereas

About the author (1999)

The author is Professor of Mathematics and Applied Mathematics at the University of Washington, Seattle, Wash.

Bibliographic information

QR code for Network Flows and Monotropic Optimization
TitleNetwork Flows and Monotropic Optimization
Volume 9 of Series on optimization, computation, and control
AuthorR. Tyrell Rockafellar
PublisherAthena Scientific, 1999
ISBN188652906X, 9781886529069
Length634 pages
Subjects ›  › 

Computers / Data Science / Data Analytics
Mathematics / Optimization
  
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