Conjugate Gradient Algorithms in Nonconvex Optimization

• Main Author: Pytlak, RadosBaw. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Nonconvex Optimization and Its Applications, 89
• Subjects: Mathematics.; Mathematical optimization.; System safety.; Calculus of Variations and Optimal Control; Optimization.; Operations Research/Decision Theory.; Quality Control, Reliability, Safety and Risk.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-85634-4

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 l...

Table of Contents:

• Conjugate directions methods for quadratic problems
• Conjugate gradient methods for nonconvex problems
• Memoryless quasi-Newton methods
• Preconditioned conjugate gradient algorithms
• Limited memory quasi-Newton algorithms
• A method of shortest residuals and nondifferentiable optimization
• The method of shortest residuals for smooth problems
• The preconditioned shortest residuals algorithm
• Optimization on a polyhedron
• Problems with box constraints
• The preconditioned shortest residuals algorithm with box
• Conjugate gradient reduced-Hessian method
• Elements of topology and analysis
• Elements of linear algebra.