Optimization Algorithms on Matrix Manifolds 

Many problems in science and engineering can be reformatted into optimization problems on matrix search spaces with so-called manifold structures. This book shows how to exploit the specific structure of such problems to develop efficient numerical algorithms. It carefully emphasizes both the algorithm’s numerical formula and its differential geometry abstraction, illustrating how good algorithms also derive insights from differential geometry, optimization, and numerical analysis. . The other two theoretical chapters provide the reader with the basic knowledge of differential geometry necessary for algorithm development. In other chapters, some well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a general development of each of these methods, drawing on material from the geometry chapters. It then guides the reader through calculations that transform these geometric formula methods into specific numerical algorithms. The most modern algorithms are given as examples that compete with the best existing algorithms for choosing eigens space problems in numerical linear algebra.
Matrix Manifolds optimization algorithms provide techniques with wide applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can be used as a college-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

optimization algorithms on matrix manifolds
optimization algorithms on matrix manifolds pdf
absil optimization algorithms on matrix manifolds
absil optimization algorithms on matrix manifolds pdf

Optimization Algorithms on Matrix Manifolds PDF

Book Description 

Many problems in science and engineering can be reformatted into optimization problems on matrix search spaces with so-called diverse structures. This book shows how to exploit the specific structure of such problems to develop efficient numerical algorithms. It carefully emphasizes both the algorithm’s numerical formula and its differential geometry abstraction, illustrating how good algorithms also derive insights from differential geometry, optimization, and numerical analysis. . The other two theoretical chapters provide the reader with the basic knowledge of differential geometry necessary for algorithm development. In other chapters, some well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a general development of each of these methods, drawing on material from the geometry chapters. It then guides the reader through calculations that transform these geometric formula methods into specific numerical algorithms. The most modern algorithms are given as examples that compete with the best existing algorithms for choosing eigens space problems in numerical linear algebra.
Matrix Manifolds optimization algorithms provide techniques with wide applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can be used as a college-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
Processing strikes the right balance between mathematical, numerical, and algorithmic perspectives. Text quality is quite high and very easy to read. This topic is very trendy and certainly of interest to the students and myself. “- Kyle A. Gallivan, Florida State University

About Author

P-A. Absil is an associate professor of mathematical engineering at the Catholic University of Louvain in Belgium. R. Mahony is a senior lecturer in engineering at the Australian National University. R. Sepulcher is Professor of Electrical Engineering and Computer Science at the University of Liège in Belgium.

Table of contents:

Foreword / by Paul van Dooren
Notation conventions
Motivation and applications
Matrix manifolds : first-order geometry
Line-search algorithms on manifolds
Matrix manifolds : second-order geometry
Newton’s method
Trust-region methods
A constellation of superlinear algorithms
Elements of linear algebra, topology, and calculus.

Optimization algorithms on matrix manifolds

Author(s): Sepulchre, Rodolphe;Absil, P.-A;Mahony, Robert

Publisher: Princeton University Press, Year: 2008

ISBN: 9780691132983,0691132984


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