Conjugate Gradient Algorithms in Nonconvex Optimization

Conjugate Direction Methods for Quadratic Problems.- Conjugate Gradient Methods for Nonconvex Problems.- Memoryless Quasi-Newton Methods.- Preconditioned Conjugate Gradient Algorithms.- Limited Memory Quasi-Newton Algorithms.- The Method of Shortest Residuals and Nondifferentiable Optimization.- The Method of Shortest Residuals for Differentiable Problems.- The Preconditioned Shortest Residuals Algorithm.- Optimization on a Polyhedron.- Conjugate Gradient Algorithms for Problems with Box Constraints.- Preconditioned Conjugate Gradient Algorithms for Problems with Box Constraints.- Preconditioned Conjugate Gradient Based Reduced-Hessian Methods.

From the reviews:

"The book describes important algorithms for the numerical treatment of unconstrained nonlinear optimization problems with many variables. ... This monograph is suitable as a text for a graduate course in computational optimization. It is useful to anyone active in this field. ... This book is well written and well organized. The argument is clear. Lists of algorithms as well as tables and figures facilitate for the reader the search for desired information in the text. The reference list is comprehensive and contains 214 items." (Sven-Åke Gustafson, Mathematical Reviews, Issue 2009 i)

"It is a very nice written book which can be used by researchers in optimization, in the teaching for seminars and by students ... . Lists of figures, tables and algorithms make this book to a useful compendium for research and teaching. A lot of bibliographical hints with respect to a large reference list make the reader known with the historical development of CG-methods ... . appendices with elements of topology, analysis, linear algebra and numerics of linear algebra make it to a self-contained book." (Armin Hoffmann, Zentralblatt MATH, Vol. 1171, 2009)