Modern optimization methods

Author: Xu Chengxian
Publisher:
Publish Date: 2004-02-01
Features: This book provides a systematic introduction to the algorithms, related techniques, and theories of nonlinear optimization. The book is divided into seven chapters. Chapter 1 discusses the fundamental theory of optimization, primarily focusing on optimality conditions; Chapter 2 introduces common numerical techniques that constitute the basic elements of various optimization algorithms, including solving linear systems, matrix factorization and matrix modification, linear search techniques, and solving trust-region subproblems; Chapters 3 to 5 introduce unconstrained optimization algorithms, mainly including quasi-Newton methods for solving medium-scale optimization problems, conjugate gradient methods for large-scale optimization problems, limited-memory quasi-Newton methods, and Gauss-Newton class algorithms that leverage the special structure of nonlinear least-squares problems; Chapters 6 and 7 discuss algorithms for constrained optimization problems. Chapter 6 primarily focuses on linear constrained optimization problems, with a focus on feasible point algorithms based on elimination methods, while Chapter 7 introduces algorithms for general nonlinear constrained optimization problems, including penalty function methods, multiplier methods, feasible direction methods, and SQP methods. This book can serve as a teaching or reference material for graduate students, senior undergraduate students in computational mathematics, applied mathematics, various engineering fields, and certain liberal arts disciplines such as finance and economics. It can also be used as a reference for engineers engaged in optimization technology applications.