Linear Programming and Network Flows, now in its third edition, addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequility constraints. This book: * Provides methods for modeling complex problems via effective algorithms on modern computers. * Presents the general theory and characteristics of optimization problems, along with effective solution algorithms. * Explores linear programming (LP) and network flows, employing polynomial-time algorithms and various specializations of the simplex method.
Table of Contents:
One: Introduction. Two: Linear Algebra, Convex Analysis, and Polyhedral Sets. Three: The Simplex Method. Four: Starting Solution and Convergence. Five: Special Simplex Implementations and Optimality Conditions. Six: Duality and Sensitivity Analysis. Seven: The Decomposition Principle. Eight: Complexity of the Simplex Algorithms. Nine: Minimal-Cost Network Flows. Ten: The Transportation and Assignment Problems. Eleven: The Out-of-Kilter Algorithm. Twelve: Maximal Flow, Shortest Path, Multicommodity Flow, and Network Synthesis Problems. Bibliography. Index.
