•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