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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.
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.
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