| Introduction | p. 1 |
| Some Issues in Linear Computation | p. 7 |
| Three Examples of Linear Computation | p. 13 |
| Gargantuan Liquids, Inc | p. 13 |
| Oil Refineries, bpd | p. 15 |
| Save Berlin, usw | p. 20 |
| The Linear Programming Problem | p. 25 |
| Standard and Canonical Forms | p. 26 |
| Matrices, Vectors, Scalars | p. 27 |
| Basic Concepts | p. 33 |
| A Fundamental Theorem | p. 36 |
| Notational Conventions and Illustrations | p. 39 |
| Five Preliminaries | p. 43 |
| Bases and Basic Feasible Solutions | p. 43 |
| Detecting Optimality | p. 43 |
| Detecting Unboundedness | p. 44 |
| A Rank-One Update | p. 45 |
| Changing Bases | p. 45 |
| Simplex Algorithms | p. 49 |
| Notation, Reading Instructions, Updating | p. 50 |
| Big M or How to Get Started | p. 54 |
| Selecting a Pivot Row and Column | p. 56 |
| Data Structures, Tolerances, Product Form | p. 58 |
| Equation Format and Cycling | p. 63 |
| Finiteness of a Simplex Algorithm | p. 69 |
| Canonical Form | p. 71 |
| A Worst-Case Example for a Simplex Algorithm | p. 75 |
| Block Pivots and Structure | p. 77 |
| A Generalized Product Form | p. 79 |
| Upper Bounds | p. 82 |
| Primal-Dual Pairs | p. 87 |
| Weak Duality | p. 89 |
| Strong Duality | p. 91 |
| Economic Interpretation and Applications | p. 94 |
| Solvability, Redundancy, Separability | p. 97 |
| A Dual Simplex Algorithm | p. 103 |
| Correctness, Finitenoss, Initialization | p. 105 |
| Post-Optimality | p. 109 |
| A Dynamic Simplex Algorithm | p. 114 |
| Analytical Geometry | p. 121 |
| Points, Linos, Subspaces | p. 124 |
| Polyhedra, Ideal Descriptions, Cones | p. 131 |
| Faces, Valid Equations, Affine Hulls | p. 134 |
| Facets, Minimal Complete Descriptions, Quasi-Uniqueness | p. 138 |
| Asymptotic Cones and Extreme Rays | p. 141 |
| Adjacency I, Extreme Rays of Polyhedra, Homogenization | p. 144 |
| Point Sets, Affine Transformations, Minimal Generators | p. 147 |
| Displaced Cones, Adjacency II, Images of Polyhedra | p. 150 |
| Carathéodory, Minkowski, Weyl | p. 155 |
| Minimal Generators, Canonical Generators, Quasi-Uniqueness | p. 157 |
| Double Description Algorithms | p. 165 |
| Correctness and Finitenoss of the Algorithm | p. 168 |
| Geometry, Euclidean Reduction, Analysis | p. 173 |
| The Basis Algorithm and All-Integer Inversion | p. 180 |
| An All-Integer Algorithm for Double Description | p. 183 |
| Digital Sizes of Rational Polyhedra and Linear Optimization | p. 188 |
| Facet Complexity, Vertex Complexity, Complexity of Inversion | p. 190 |
| Polyhedra and Related Polytopes for Linear Optimization | p. 194 |
| Feasibility, Binary Search, Linear Optimization | p. 197 |
| Perturbation, Uniqueness, Separation | p. 202 |
| Geometry and Complexity of Simplex Algorithms | p. 207 |
| Pivot Column Choice, Simplex Paths, Big M Revisited | p. 208 |
| Gaussian Elimination, Fill-In, Scaling | p. 212 |
| Iterative Step I, Pivot Choice, Cholesky Factorization | p. 216 |
| Cross Multiplication, Iterative Step II, Integer Factorization | p. 219 |
| Division Free Gaussian Elimination and Cramer's Rule | p. 221 |
| Circles, Spheres, Ellipsoids | p. 229 |
| Projective Algorithms | p. 239 |
| A Basic Algorithm | p. 243 |
| The Solution of the Approximate Problem | p. 245 |
| Convergence of the Approximate Iterates | p. 246 |
| Correctness, Finiteness, Initialization | p. 250 |
| Analysis, Algebra, Geometry | p. 253 |
| Solution to the Problem in the Original Space | p. 254 |
| The Solution in the Transformed Space | p. 260 |
| Geometric Interpretations and Properties | p. 264 |
| Extending the Exact Solution and Proofs | p. 268 |
| Examples of Projective Images | p. 271 |
| The Cross Ratio | p. 274 |
| Reflection on a Circle and Sandwiching | p. 278 |
| The Iterative Step | p. 283 |
| A Projective Algorithm | p. 288 |
| Centers, Barriers, Newton Steps | p. 292 |
| A Method of Centers | p. 296 |
| The Logarithmic Barrier Function | p. 298 |
| A Newtonian Algorithm | p. 303 |
| Coda | p. 308 |
| Ellipsoid Algorithms | p. 309 |
| Matrix Norms, Approximate Inverses, Matrix Inequalities | p. 316 |
| Ellipsoid "Halving" in Approximate Arithmetic | p. 320 |
| Polynomial-Time Algorithms for Linear Programming | p. 328 |
| Linear Programming and Binary Search | p. 336 |
| Deep Cuts, Sliding Objective, Large Steps, Line Search | p. 339 |
| Linear Programming the Ellipsoidal Way: Two Examples | p. 344 |
| Correctness and Finiteness of the DCS Ellipsoid Algorithm | p. 348 |
| Optimal Separators, Most Violated Separators, Separation | p. 352 |
| ¿-Solidification of Flats, Polytopal Norms, Rounding | p. 356 |
| Rational Rounding and Continued Fractions | p. 361 |
| Optimization and Separation | p. 368 |
| ¿-Optimal Sets and ¿-Optimal Solutions | p. 371 |
| Finding Direction Vectors in the Asymptotic Cone | p. 373 |
| A CCS Ellipsoid Algorithm | p. 375 |
| Linear Optimization and Polyhedral Separation | p. 378 |
| Combinatorial Optimization: An Introduction | p. 387 |
| The Berlin Airlift Model Revisited | p. 389 |
| Complete Formulations and Their Implications | p. 396 |
| Extremal Characterizations of Ideal Formulations | p. 405 |
| Blocking and Antiblocking Polyhedra | p. 414 |
| Polyhedra with the Integrality Property | p. 417 |
| Appendices | |
| Short-Term Financial Management | p. 423 |
| Operations Management in a Refinery | p. 427 |
| Automatized Production: PCBs and Ulysses' Problem | p. 441 |
| References | p. 457 |
| Bibliography | p. 479 |
| Index | p. 495 |
| Table of Contents provided by Publisher. All Rights Reserved. |
