## Linear Programs and Related ProblemsThis text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples. |

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### Contents

Introduction | 3 |

Tableau Algebra | 43 |

Canonical Duality | 95 |

The Simplex Algorithm | 145 |

General Linear Programs | 177 |

Numerical Considerations | 209 |

Matrix Games | 253 |

Assignment and Matching Problems | 275 |

The Transportation Problem | 319 |

Network Flow Problems | 373 |

The Transshipment Problem | 395 |

Nonlinear Programs | 419 |

A Answers | 493 |

575 | |

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### Common terms and phrases

6-entry artificial variables assignment problem basement row basic solution basic variables c-row canonical choice column equations column system complementary computed Consider constraints corresponding dual linear programs dual pair dual problem dual program dual variables equivalent tableaux example feasibility specifications feasible set Figure finite number free free game matrix graph Hungarian algorithm hyperplane infeasible row initial tableau Karush-Kuhn-Tucker conditions label least left margin linear complementarity problem linear programming problem loop matrix game max program maximize maximum minimize minimum negative entry node nonbasic variables nonlinear program nonnegative 6-column nonpositive nonzero entry objective variable obtain optimal solution optimal strategies permutation matrix pivot column pivot entry pivot row positive entry positive semidefinite principal pivot exchange program is feasible represented row and column row equations row system rule Section simplex algorithm slack variables solve starred zero system of equations Theorem top margin transportation problem