an:05223994
Zbl 1147.65043
Absil, P.-A.; Mahony, R.; Sepulchre, R.
Optimization algorithms on matrix manifolds
EN
Princeton, NJ: Princeton University Press (ISBN 978-0-691-13298-3/hbk). xv, 224~p. (2008).
2008
b
65K05 65-02 90-02 90C51 90C53 90C30
mathematical programming; textbook
This book has 224 pages and it is divided into an Introduction and seven chapters, namely: Chapter 2: Motivation and applications (p. 5); Chapter 3: Matrix manifolds: First-order geometry (p.~17); Chapter 4: Line search algorithms on manifolds (p.~54); Chapter 5: Matrix manifolds: Second-order geometry (p.~91); Chapter 6: Newton's method (p.~91); Chapter 7: Trust-region methods (p.~136); Chapter 8: A constellation of superlinear algorithms (p. 168--198).
Many problems in the science and engineering can be rephrased as optimization problems on a matrix search space endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms and to give differential geometric interpretations. Chapters 3, 4 and 5 offer differential geometry notions necessary to the algorithmic developments. The book presents applicative domains to mathematicians, engineers and computer scientists.
Stefan Mititelu (Bucure??ti)