Buch, Englisch, 965 Seiten, Format (B × H): 155 mm x 235 mm
Buch, Englisch, 965 Seiten, Format (B × H): 155 mm x 235 mm
Reihe: Springer Optimization and Its Applications
ISBN: 978-3-032-41213-3
Verlag: Springer
This book is devoted to gradient methods for continuous optimization, offering a comprehensive analysis and algorithmic implementation of techniques for minimizing various types of objective functions, both constrained and unconstrained. At its core, the book addresses the challenge of efficiently solving technical, scientific, and economic problems through continuous optimization.
Readers will explore key concepts such as descent direction methods, trust region methods, and cubic regularization methods, with particular attention given to solving systems of nonlinear equations and optimization methods for dynamic systems. The book also delves into the intricacies of sparse and nonsmooth objective functions, providing insights into the use of automatic differentiation and numerical differentiation. With contributions from experienced practitioners, this volume is a must-read for those seeking to understand the latest advancements in optimization techniques. Almost all of the methods presented in this book have been implemented, thoroughly tested, and compared with one another.
The results of these tests are presented and discussed throughout the book. Ideal for researchers, scholars, and students in the fields of mathematics, computer science, and engineering, this book serves as both a comprehensive monograph and a valuable teaching aid.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Introduction to Unconstrained Optimization.- Descent Direction Methods.- Conjugate Gradient Methods.- Variable Metric Methods.- Trust Region Methods.- Computation of Trust Region Direction Vectors.- Cubic Regularization Methods.- Methods for Minimizing the Sum of Squares.- Limited Memory Variable Metric Methods.- Discrete Newton Methods in Vector Form.-Methods for Large-Scale Sparse Problems.- Methods for Large-Scale Partially Separable Problems.- Methods for Large-Scale Sums of Squares.- Methods for Solving Systems of Nonlinear Equations.- Methods for Large-Scale Systems of Nonlinear Equations.- Optimization of Dynamic Systems.- Automatic and Numerical Differentiation.- Fundamentals of Nonsmooth Analysis.- Methods for Solving Systems of Nonsmooth Equations.- Bundle Methods for General Nonsmooth Optimization Problems.- Introduction to Nonlinear Programming.-Minimization with Linear Constraints.- Minimization with equality constraints.- General Nonlinear Programming Problems.- Generalized Minimax Problems.
