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Linear Programming Computation de Ping-Qi PAN

Linear Programming Computation

Autor Ping-Qi PAN
en Limba Engleză Hardback – 2 ian 2023

ABORDAREA PRACTICĂ: Linear Programming Computation se distinge prin echilibrul riguros între fundamentarea teoretică și eficiența computațională, oferind o perspectivă tehnică asupra evoluției algoritmilor de la George Dantzig până în prezent. Remarcăm că această a doua ediție nu se rezumă la o simplă trecere în revistă a conceptelor, ci prioritizează implementarea codului și validarea prin rezultate numerice. Structura lucrării, extinsă acum la două volume, reflectă o progresie logică: de la geometria regiunii fezabile și metoda simplex clasică în prima parte, către contribuții de ultimă oră precum metodele de bază deficitară sau algoritmii de tip „face method”. Pe linia practică a volumului Computer Solution of Linear Programs, dar cu focus pe noile tehnici de pivotare și metodele simplex reduse, autorul Ping-Qi PAN transformă complexitatea matematică în soluții aplicabile. Reținem importanța capitolului dedicat programării liniare întregi (ILP), complet rescris pentru a include metodele de ramificare și tăiere controlată (controlled-cutting/branch), esențiale pentru noii solveri. De asemenea, introducerea factorizării LU pentru gestionarea matricelor rare (sparse computation) indică orientarea clară a cărții către performanța în sistemele de calcul reale. Este o resursă care documentează minuțios tranziția de la teorie la execuție, fiind susținută de experimente computaționale ce confirmă superioritatea noilor reguli de pivotare propuse.

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Specificații

ISBN-13: 9789811901461
ISBN-10: 9811901465
Pagini: 737
Ilustrații: XXVIII, 737 p. 1 illus. In 2 volumes, not available separately.
Dimensiuni: 155 x 235 x 56 mm
Greutate: 1.43 kg
Ediția:2nd ed. 2023
Editura: Springer Nature Singapore
Colecția Springer
Locul publicării:Singapore, Singapore

De ce să citești această carte

Pentru specialiștii în optimizare și dezvoltatorii de software matematic, această carte oferă acces la algoritmi de ultimă generație care depășesc performanțele metodelor clasice. Cititorul câștigă o înțelegere profundă a implementării practice, învățând cum să gestioneze calculele complexe prin factorizări eficiente și noi reguli de pivotare, elemente critice pentru crearea unor solveri de mare viteză.

Despre autor

Ping-Qi PAN este un cercetător recunoscut în domeniul optimizării matematice, a cărui activitate a influențat semnificativ stadiul actual al programării liniare. Prin publicațiile sale și contribuțiile originale, precum dezvoltarea metodei simplex reduse și a tehnicilor de pivotare duală, autorul a adus îmbunătățiri majore eficienței computaționale în rezolvarea problemelor de optimizare pe scară largă. Experiența sa academică și practică este reflectată în rigoarea cu care tratează factorizarea matricelor și implementarea algoritmilor în acest volum de referință publicat de Springer.

Descriere scurtă

This monograph represents a historic breakthrough in the field of linear programming (LP)since George Dantzig first discovered the simplex method in 1947.
Being both thoughtful and informative, it focuses on reflecting and promoting the state of the art by highlighting new achievements in LP. This new edition is organized in two volumes. The first volume addresses foundations of LP, including the geometry of feasible region, the simplex method and its implementation, duality and the dual simplex method, the primal-dual simplex method, sensitivity analysis and parametric LP, the generalized simplex method, the decomposition method, the interior-point method and integer LP method. The second volume mainly introduces contributions of the author himself, such as efficient primal/dual pivot rules, primal/dual Phase-I methods, reduced/D-reduced simplex methods, the generalized reduced simplex method, primal/dual deficient-basis methods, primal/dual face methods, a new decomposition principle, etc.
Many important improvements were made in this edition. The first volume includes new results, such as the mixed two-phase simplex algorithm, dual elimination, fresh pricing scheme for reduced cost, bilevel LP models and intercepting of optimal solution set. In particular, the chapter Integer LP Method was rewritten with great gains of the objective cutting for new ILP solvers {\it controlled-cutting/branch} methods, as well as with an attractive implementation of the controlled-branch method.
In the second volume, the `simplex feasible-point algorithm' was rewritten, and removed from the chapter Pivotal Interior-Point Method to form an independent chapter with the new title `Simplex Interior-Point Method', as it represents a class of efficient interior-point algorithms transformed from traditional simplex algorithms. The title of the original chapter was then changed to `Facial Interior-Point Method', as the remaining algorithms represent another class of efficient interior-point algorithms transformed from normal interior-point algorithms. Without exploiting sparsity, the original primal/dual face methods were implemented using Cholesky factorization. In order to deal with sparse computation, two new chapters discussing LU factorization were added to the second volume. The most exciting improvement came from the rediscovery of the reduced simplex method. In the first edition, the derivation of its prototype was presented in a chapter with the same title, and then converted into the so-called `improved' version in another chapter. Fortunately, the author recently found a quite concise new derivation, so he can now introduce the distinctive fresh simplex method in a single chapter. It is exciting that the reduced simplex method can be expected to be the best LP solver ever.
With a focus on computation, the current edition contains many novel ideas, theories and methods, supported by solid numerical results. Being clear and succinct, its content reveals in a fresh manner, from simple to profound. In particular, a larger number of examples were worked out to demonstrate algorithms. This book is a rare work in LP and an indispensable tool for undergraduate and graduate students, teachers, practitioners, and researchers in LP and related fields.

Cuprins

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.

Notă biografică

Ping-Qi Pan is Professor and Doctoral Supervisor of Mathematics Department at Southeast University, Nanjing, China. He was Visiting Scholar at University of Washington (1986–1987), and Visiting Scientist at Cornell University (1987–1988). His research interest focuses on mathematical programming and operations research, especially large-scale linear optimization. He was standing council member of Mathematical Programming Society of China, and standing council member of Operation Research Society of China. Professor Pan has received the honorary title of Outstanding Scientific-Technical Worker of Jiangsu Province of China. He was nominated as Top 100 scientist of 2012 by the International Biographical Centre, Cambridge, England. He won the LIFETIME ACHIEVEMENT AWARD by Who’s Who in the World in 2017.

Textul de pe ultima copertă

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.

Caracteristici

A landmark work on LP An updated edition with important improvements A must-read for students, researchers, and practitioners interested in LP and related areas

Recenzii

“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)