Linear programming computation / Ping-Qi Pan.
Pan, Ping-Qi, author.
2023
T57.74 .P36 2023
Available Online

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Title Linear programming computation / Ping-Qi Pan.
Author Pan, Ping-Qi, author.
Edition Second edition.
ISBN 9789811901478 electronic book
9811901473 electronic book
9789811901461
9811901465
DOI https://doi.org/10.1007/978-981-19-0147-8
Published Singapore : Springer, 2023.
Language English
Description 1 online resource (1 volume) : illustrations (black and white).
Other Standard Identifiers 10.1007/978-981-19-0147-8 doi
Call Number T57.74 .P36 2023
Dewey Decimal Classification 519.7/2
Summary Organized into two volumes. this book represents a real breakthrough in the field of linear programming (LP). The first volume addresses fundamentals, including geometry of feasible region, simplex method, implementation of simplex method, duality and dual simplex method, sensitivity analysis and parametric LP, generalized simplex method, decomposition method, interior-point method and integer LP method, as well as reflects the state of art by highlighting new results, such as efficient primal and dual pivot rules, primal and dual Phase-I methods. The second volume introduces contributions of the author himself, such as reduced and D-reduced-simplex methods, generalized reduced and dual reduced simplex methods, deficient-basis and dual deficient-basis-simplex methods, and face and dual face methods with Cholesky factorization, as well as with LU factorization. As a monograph, this book is a rare work in LP, containing many noval ideas and methods, supported by complete computational results. As revealed from the perspective of theory, the most recently achieved results, such as reduced and D-reduced simplex methods, as well as ILP solvers--- controlled-cut and controlled-branch methods, are very significant and promising, though there are no computational results available at this stage. With a focus on computation, the content of this book ranges from simple to profound, clear and fresh. In particular, all algorithms are accompanied by examples for demonstration whenever possible. As a milestone of LP, this book is an indispensable tool for undergraduate and graduate students, teachers, practitioners and researchers, in LP and related fields.
Note Previous edition: 2014.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Available in Other Form Linear programming computation.
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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.

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