Linear programming using MATLAB®
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 num...
| Main Author: | Ploskas, Nikolaos, (Author) |
|---|---|
| Other Authors: | Samaras, Nikolaos,, SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer,
2017.
|
| Physical Description: |
1 online resource (xvii, 637 pages) : illustrations (some color). |
| Series: |
Springer optimization and its applications ;
v. 127. |
| Subjects: |
| Summary: |
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.-- |
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| Item Description: |
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. 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.-- Provided by publisher. |
| Physical Description: |
1 online resource (xvii, 637 pages) : illustrations (some color). |
| ISBN: |
9783319659190 3319659197 |
| ISSN: |
1931-6828 ; |