## Large Scale Linear and Integer Optimization: A Unified ApproachThis is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

LINEAR SYSTEMS AND PROJECTION 35 | 34 |

PROJECTION | 81 |

THE SIMPLEX ALGORITHM | 143 |

MORE ON SIMPLEX 183 | 182 |

INTEGER PROGRAMMING | 313 |

DANTZIGWOLFE | 369 |

LAGRANGIAN METHODS | 393 |

NETWORK FLOW LINEAR PROGRAMS | 481 |

A POLYHEDRAL THEORY 635 | 634 |

COMPLEXITY THEORY | 657 |

Complexity Classes | 663 |

Aſ PCompleteness | 669 |

BASIC GRAPH THEORY | 677 |

686 | |

723 | |

### Other editions - View all

Large Scale Linear and Integer Optimization: A Unified Approach Richard Kipp Martin No preview available - 2012 |

Large Scale Linear and Integer Optimization: A Unified Approach Richard Kipp Martin No preview available - 1998 |

### Common terms and phrases

Assume auxiliary variables basic feasible solution basic variable Benders binary branch-and-bound calculate candidate problem Chapter column cone conv(T convex corresponding decomposition defined dual variables dynamic lot equation Euclidean algorithm Example extreme point extreme ray formulation Gaussian elimination given graph Hermite normal form implies inequalities infeasible integer linear program integer polyhedron integer programming integer solution integer variables integer vector inverse projection iteration knapsack knapsack problem Lagrangian Lagrangian dual Lemma linear programming relaxation lower bound LU decomposition method minimal network flow network flow problem nonbasic variables nonnegative nonzero elements objective function value OOOOOO optimal solution value path following algorithm pivot polyhedral polynomial polytope primal solution Proof Proposition restricted master result right hand side Section simplex algorithm slack solving Step subproblem subset system Aa totally unimodular update upper bound vertex zero