This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference.
Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke–Jeeves, implicit filtering, MDS, and Nelder–Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.
Optimization problems abound in science and engineering, and this book provides an efficient introduction to the fundamental ideas for the practicing engineer or scientist. Readers should be familiar with the material in an elementary graduate level course in numerical analysis and with local convergence results for systems of nonlinear equations.
Preface; How to Get the Software; Part I: Optimization of Smooth Functions; Chapter 1: Basic Concepts; Chapter 2: Local Convergence of Newton's Method; Chapter 3: Global Convergence; Chapter 4: The BFGS Method; Chapter 5: Simple Bound Constraints; Part II: Optimization of Noisy Functions; Chapter 6: Basic Concepts and Goals; Chapter 7: Implicit Filtering; Chapter 8: Direct Search Algorithms; Bibliography; Index.
About the Author
C.T. Kelley is a Professor in the Department of Mathematics and Center for Research in Scientific Computation at North Carolina State University. He is a member of the editorial board of the SIAM Journal on Optimization, and the SIAM Journal on Numerical Analysis and is the author of over 100 papers and proceedings articles on numerical and computational mathematics.
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