Linear and Nonlinear Programming: Second Edition

ISBN-13: 9781402075933 / Angielski / Twarda / 2003 / 492 str.

David G. Luenberger; D. G. Luenberger

Opis

The original edition of this book was celebrated for its coverage of the central concepts of practical optimization techniques. This updated edition expands and illuminates the connection between the purely analytical character of an optimization problem, expressed by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. Incorporating modern theoretical insights, this classic text is even more useful.

Recenzje

From the reviews of the second edition:

"I have profitably used the book to apply constrained minimization procedures in the field of computational contact mechanics. I think it is not a secret that quite often books on mathematics are written from mathematicians for mathematicians. Hence it is quite hard for engineers to read and to extract valuable information from them. With this respect this book is a shining star. It presents the topics in a very precise but clear and understandable way."
(Giorgio Azvaris, Turin, Italy)
"I have the 1977 edition from my father's MIT days. I am a Mathematician and I can verify that the book written in 1977 is of the same style that good books have today. A book is not made obsolete because some new "elegant" terms arise."
(A reader from Greece)

"In this second edition … David Luenberger focuses on practical optimization techniques. … the book would be appropriate for graduate students or for self-study by professionals. … I recommend the book for those who are familiar with elements of linear algebra … . The book concludes with three short appendices … and a bibliography and a short index. … is intended for those who want to look deeply into optimization techniques, linear and nonlinear. … will be useful to researchers, engineers, and graduate students." (Sergio Ubeda, Interfaces, Vol. 37 (1), 2007)

Spis treści

1. Introduction.
Part I: Linear Programming. 2. Basic Properties of Linear Programs.3. The Simplex Method. 4. Duality. 5. Transportation and Network Flow Problems.
Part II: Unconstrained Problems. 6. Basic Properties of Solutions and Algorithms. 7. Basic Descent Methods. 8. Conjugate Direction Methods. 9. Quasi- Newton Methods.
Part III: Constrained Minimization. 10. Constrained Minimization Conditions. 11. Primal Methods. 12. Penalty and Barrier Methods. 13. Dual and Cutting Plane Methods. 14. Lagrange Methods.
Appendix A: Mathematical Review. A.1. Sets. A.2. Matrix Notation. A.3. Spaces. A.4. Eigenvalues and Quadratic Forms. A.5. Topological Concepts. A.6. Functions.
Appendix B: Convex Sets. B.1. Basic Definitions. B.2. Hyperplanes and Polytopes. B.3. Separating and Supporting Hyperplanes. B.4. Extreme Points.
Appendix C: Gaussian Elimination.
Bibliography. Index.

O autorze

David G. Luenberger has directed much of his career toward teaching "portable concepts" - organizing theory around concepts and actually "porting" the concepts to applications where, in the process, the general concepts are often discovered. The search for fundamentals has explicitly directed his research in the fields of control, optimization, planning, economics, and investments, and in turn, it is the discovery of these fundamentals that have motivated his textbook writing projects.