## Network Flows and Monotropic OptimizationA 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 |

### Contents

1 | |

26 | |

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 |

602 | |

611 | |