•Networks

1.Definition of a Network

2.Examples of Networks

3.Incidences

4.Flows

5.Divergence

6.Vector Operations

7.Circulations and the Augmented Network

8.Dynamic Version of a Network

9.Potentials and Tension

10.Preview of Optimal Flows and Potentials

11.Some Generalizations

12.Exercises

13.Comments and References

•Paths and Cuts

1.Paths

2.Incidences for Paths

3.Connectedness

4.Finding a Path from One Place to Another

5.Cuts

6.Painted Network Algorithm

7.Priority Rules and Multiroutings

8.Theoretical Implications of the Algorithm

9.Application to Connectedness

10.Acyclic Networks

11.Planar Networks and Duality

12.Exercises

13.Comments and References

•Flows and Capacities

1.Capacity Intervals

2.Flux across a Cut

3.Max Flow Problem

4.Max Flow Min Cut

5.Nature of the Min Cut Problem

6.Max Flow Algorithm

7.Commensurability and Termination

8.Feasible Flows

9.Feasible Distribution Algorithm

10.Multipath Implementation

11.Flow Rectification Algorithm

12.Node Capacities and Dynamic Flows

13.Exercises

14.Comments and References

•Analysis of Flow

1.Integral Flows

2.Conformal Realization of Flows

3.Realization Algorithm

4.Justification of the Algorithm

5.Trees

6.Forrests and Spanning Trees

7.Tucker Representations of the Circulation Space

8.Basic Theorem

9.Pivoting

10.Extreme Flows

11.Extremal Representation Algorithm

12.Exercises

13.Comments and References

•Matching Theory and Assignment Problems

1.Matching Problem

2.Matching Algorithm

3.Assignments

4.Application to Partially Ordered Sets

5.Optimal Assignments

6.Hungarian Assignment Algorithm

7.Matching with Multiplicities

8.Bottleneck Optimization

9.Exercises

10.Comments and References

•Potentials and Spans

1.Spread Relative to a Path

2.Optimal Paths

3.Max Tension Min Path

4.Min Path Algorithm

5.Node-Scanning Implementation

6.Feasible Potentials

7.Feasible Differential Theorem

8.Refinements

9.Tension Rectification Algorithm

10.Optimal Routings

11.Routing Optimization Procedure

12.Integral and Extreme Differentials

13.Exercises

14.Comments and References

•Networks with Linear Costs

1.Linear Optimal Distribution Problem

2.Examples of Optimization of Flows

3.Optimal Distribution Algorithm

4.Simplex Method for Flows

5.Linear Optimal Differential Problem

6.Examples of Optimization of Potentials

7.Optimal Differential Algorithm

8.Simplex Algorithm for Potentials

9.Duality and the Elementary Problems

10.Thrifty Adjustment Algorithm

11.Interpretations

12.Multipath Implementation

13.Out-of-Kilter Algorithm

14.Exercises

15.Comments and References

•Optimal Flows and Potentials

1.Convex Cost Functions

2.Characteristic Curves

3.Piecewise Linear or Quadratic Costs

4.Optimal Distribution Problem

5.Conjugate Costs

6.Examples of Conjugate Functions

7.Optimal Differential Problem

8.Duality Theorem and Equilibrium Conditions

9.Equilibrium Models

10.Improvement of Flows

11.Improvement of Potentials

12.Existence of Solutions

13.Boundeness of Optimizing Sequences

14.Black Boxes

15.Exercises

16.Comments and References

•Algorithms for Convex Costs

1.Optimal Distribution Algorithm

2.Application to Piecewise Linear Problems

3.Optimal Differential Algorithm

4.Thrifty Adjustment Algorithm (Piecewise Linear)

5.Application to Black Boxes

6.Out-of-Kilter Algorithm (Piecewise Linear)

7.Termination and Refinements

8.Fortified Algorithms and the Duality Theorem

9.Discretized Descent Algorithms

10.Calculating epsilon-Optimal Solutions

11.Optimizing Sequences and Piecewise Linearization

12.Convex Simplex Method

13.Exercises

14.Comments and References

•Linear Systems of Variables

1.Primal and Dual Variables

2.Elementary Vectors and Supports

3.Bases

4.Networks with Gains

5.A Generalization of Circuits and Cuts

6.Multicommodity Systems and Factorization

7.Painted Index Theorem and Algorithm

8.Termination and Preprocessing

9.Constraints and Feasibility

10.Rectification Algorithms

11.Shortcuts in Pivoting Implementation

12.Augmented and Aggregated Formats

13.Extreme Solutions

14.Exercises

15.Comments and References

•Monotropic Programming

1.Optimization and Equilibrium

2.Examples of Monotropic Programming

3.Descent by Elementary Vectors

4.Duality and the Existence of Solutions

5.Boundedness Property

6.Decomposition

7.Application to Traffic Equilibrium

8.Basic Descent Algorithms

9.Fortified and Discretized Descent

10.Simplex Methods

11.General Out-of-Kilter Algorithm

12.Other Formats and Termination

13.Parametric Programming

14.Exercises

15.Comments and References

Bibliograpgy

Index