Ping-Qi PAN

Linear Programming Computation

• Broschiertes Buch

Produktbeschreibung

With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods. In particular, it covers the determination of the optimal solution set, feasible-point simplex method, decomposition principle for solving large-scale problems, controlled-branch method based on generalized reduced simplex framework for solving integer LP problems.

Produktdetails

• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-662-51430-6
• Softcover reprint of the original 1st ed. 2014
• Seitenzahl: 768
• Erscheinungstermin: 3. September 2016
• Englisch
• Abmessung: 235mm x 155mm x 41mm
• Gewicht: 1142g
• ISBN-13: 9783662514306
• ISBN-10: 3662514303
• Artikelnr.: 45645392

Inhaltsangabe

Introduction.- Geometry of the Feasible Region.- Simplex Method.- Duality principle and dual simplex method.- Implementation of the Simplex Method.- Sensitivity Analysis and Parametric LP.- Variants of the Simplex Method.- Decomposition Method.- Interior Point Method.- Integer Linear Programming (ILP).- Pivot Rule.- Dual Pivot Rule.- Simplex Phase-I Method.- Dual Simplex Phase-l Method.- Reduced Simplex Method.- Improved Reduced Simplex Method.- D-Reduced Simplex Method.- Criss-Cross Simplex Method.- Generalizing Reduced Simplex Method.- Deficient-Basis Method.- Dual Deficient-Basis Method.- Face Method.- Dual Face Method.- Pivotal interior-point Method.- Special Topics.- Appendix.- References.

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Chapter 1. Introduction.- Chapter 2. Geometry of Feasible Region.- Chapter 3. Simplex Method.- Chapter 4. Implementation of Simplex Method.- Chapter 5. Duality Principle and Dual Simplex Method.- Chapter 6. Primal-Dual Simplex Method.- Chapter 7. Sensitivity Analysis and Parametric LP.- Chapter 8. Generalized Simplex Method.- Chapter 9. Decomposition Method.- Chapter 10. Interior-Point Method.- Chapter 11. Integer Linear Programming (ILP).- Chapter 12. Pivot Rule.- Chapter 13. Dual Pivot Rule.- Chapter 14. Simplex Phase-I Method.- Chapter 15. Dual Simplex Phase-l Method.- Chapter 16. Reduced Simplex Method.- Chapter 17. D-Reduced Simplex Method.- Chapter 18. Generalized Reduced Simplex Method.- Chapter 19. Deficient-Basis Method.- Chapter 20. Dual Decient-Basis Method.- Chapter 21. Face Method with Cholesky Factorization.- Chapter 22. Dual Face Method with Cholesky Factorization.- Chapter 23. Face Method with LU Factorization.- Chapter 24. Dual Face Method with LU Factorization.- Chapter 25. Simplex Interior-Point Method.- Chapter 26. Facial Interior-Point Method.- Chapter 27. Decomposition Principle.

Rezensionen

"Evidenced by superior performance in computational experiments, the author's work has refreshed the state of the art of LP, and by its originality, breadth and depth, is having a major impact on the field of mathematical optimization." (EJOR, European Journal of Operational Research, Vol. 267 (3), June, 2018)

"The book seems to be mainly addressed to scientists who already possess some expertise in LP. The kind of presentation, however, also allows using parts of it as a basis for a course on the topic. In fact, a special feature of the book is that an algorithm typically is accompanied by some example for which the results of all computational steps needed to find a solution are written down." (Rembert Reemtsen, zbMATH, Vol. 1302, 2015)

"This book is a research monograph focusing on computational techniques in the simplex method for linear programming. ... It may be of interest to researchers and developers of simplex method codes for linear programming." (B. Borchers, Choice, Vol. 52 (3), November, 2014)