Conjugate Gradient Algorithms in Nonconvex Optimization

Radosław Pytlak (auth.)9783540856337, 3540856331, 354085634X, 9783540856344

This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective.

Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms.

The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented.

Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book.

Table of contents :
Front Matter….Pages i-xxvi
Conjugate Direction Methods for Quadratic Problems….Pages 1-62
Conjugate Gradient Methods for Nonconvex Problems….Pages 63-108
Memoryless Quasi-Newton Methods….Pages 109-131
Preconditioned Conjugate Gradient Algorithms….Pages 134-158
Limited Memory Quasi-Newton Algorithms….Pages 159-190
The Method of Shortest Residuals and Nondifferentiable Optimization….Pages 191-215
The Method of Shortest Residuals for Differentiable Problems….Pages 217-278
The Preconditioned Shortest Residuals Algorithm….Pages 279-297
Optimization on a Polyhedron….Pages 299-325
Conjugate Gradient Algorithms for Problems with Box Constraints….Pages 327-369
Preconditioned Conjugate Gradient Algorithms for Problems with Box Constraints….Pages 371-398
Preconditioned Conjugate Gradient Based Reduced-Hessian Methods….Pages 399-428
Back Matter….Pages 429-477