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Nonlinear Conjugate Gradient Methods for Unconstrained Optimization (Paperback, 1st ed. 2020)
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Nonlinear Conjugate Gradient Methods for Unconstrained Optimization (Paperback, 1st ed. 2020)
Series: Springer Optimization and Its Applications, 158
Expected to ship within 10 - 15 working days
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Two approaches are known for solving large-scale unconstrained
optimization problems-the limited-memory quasi-Newton method
(truncated Newton method) and the conjugate gradient method. This
is the first book to detail conjugate gradient methods, showing
their properties and convergence characteristics as well as their
performance in solving large-scale unconstrained optimization
problems and applications. Comparisons to the limited-memory and
truncated Newton methods are also discussed. Topics studied in
detail include: linear conjugate gradient methods, standard
conjugate gradient methods, acceleration of conjugate gradient
methods, hybrid, modifications of the standard scheme, memoryless
BFGS preconditioned, and three-term. Other conjugate gradient
methods with clustering the eigenvalues or with the minimization of
the condition number of the iteration matrix, are also treated. For
each method, the convergence analysis, the computational
performances and the comparisons versus other conjugate gradient
methods are given. The theory behind the conjugate gradient
algorithms presented as a methodology is developed with a clear,
rigorous, and friendly exposition; the reader will gain an
understanding of their properties and their convergence and will
learn to develop and prove the convergence of his/her own methods.
Numerous numerical studies are supplied with comparisons and
comments on the behavior of conjugate gradient algorithms for
solving a collection of 800 unconstrained optimization problems of
different structures and complexities with the number of variables
in the range [1000,10000]. The book is addressed to all those
interested in developing and using new advanced techniques for
solving unconstrained optimization complex problems. Mathematical
programming researchers, theoreticians and practitioners in
operations research, practitioners in engineering and industry
researchers, as well as graduate students in mathematics, Ph.D. and
master students in mathematical programming, will find plenty of
information and practical applications for solving large-scale
unconstrained optimization problems and applications by conjugate
gradient methods.
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