Optimization algorithms on matrix manifolds
Algorithms Mathematical optimization Matrices e-böcker
Princeton University Press
2008
EISBN 9781400830244
Introduction.
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.
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differentia.
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.
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differentia.
