Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold…
Specifikacia Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. 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. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.
In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. The book provides a generic development of each of these methods, building upon the material of
Algorithms for Convex Optimization
Calculus On Manifolds
Analysis On Manifolds
Analysis On Manifolds
Stochastic Analysis on Manifolds