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This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms.
As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.
Inhaltsverzeichnis
1. Introduction.- 2. Linear Programming Algorithms.- 3. Linear Programming Benchmark and Random Problems.- 4. Presolve Methods.- 5. Scaling Techniques.- 6. Pivoting Rules.- 7. Basis Inverse and Update Methods.- 8. Revised Primal Simplex Algorithm.- 9. Exterior Point Simplex Algorithms.- 10. Interior Point Method.- 11. Sensitivity Analysis.- Appendix: MATLAB's Optimization Toolbox Algorithms.- Appendix: State-of-the-art Linear Programming Solvers;CLP and CPLEX.
Über den Autor / die Autorin
Bette LaPlante and Diane Cuvelier are the founders of Doughmakers Gourmet Bakeware, a company that produces high-quality pizza, pie, cake, and muffin pans. The Doughmakers have been profiled in Women's Day, People, Southern Living, Taste of Home, Gourmet, and many others. They live with their families in Terre Haute, Indiana.
Bette LaPlante and Diane Cuvelier are the founders of Doughmakers Gourmet Bakeware, a company that produces high-quality pizza, pie, cake, and muffin pans. The Doughmakers have been profiled in Women's Day, People, Southern Living, Taste of Home, Gourmet, and many others. They live with their families in Terre Haute, Indiana.
Zusammenfassung
Methodically presents all components of the simplex-type methods
Enables readers to experiment with MATLAB® codes that are able to solve large-scale benchmark linear programs
Contains 11 presolve techniques, 11 scaling techniques, 6 pivoting rules, and 4 basis inverse and update methods
