Optimization Theory and Methods：Nonlinear Programming
Optimization is a subject that is widely and increasingly used in science,
engineering, economics, management, industry, and other areas. It deals
with selecting the best of many possible decisions in real-life environment,
constructing computational methods to find optimal solutions, exploring the
theoretical properties, and studying the computational performance of numerical
algorithms implemented based on computational methods.
Along with the rapid development of high-performance computers and
progress of computational methods, more and more large-scale optimization
problems have been studied and solved. As pointed out by Professor Yuqi He
of Harvard University, a member of the US National Academy of Engineering,
optimization is a cornerstone for the development of civilization.
This book systematically introduces optimization theory and methods,
discusses in detail optimality conditions, and develops computational methods
for unconstrained, constrained, and nonsmooth optimization. Due to
limited space, we do not cover all important topics in optimization. We
omit some important topics, such as linear programming, conic convex programming,
mathematical programming with equilibrium constraints, semiinfinite
programming, and global optimization. Interested readers can refer
to Dantzig [78], Walsch [347], Shu-Cheng Fang and S. Puthenpura [121], Luo,
Pang, and Ralph [202], Wright [358], Wolkowitz, Saigal, and Vandenberghe
[355].
The book contains a lot of recent research results on nonlinear programming
including those of the authors, for example, results on trust region
methods, inexact Newton method, self-scaling variable metric method, conic
model method, non-quasi-Newton method, sequential quadratic programming,
and nonsmooth optimization, etc.. We have tried to make the book
xii PREFACE
self-contained, systematic in theory and algorithms, and easy to read. For
most methods, we motivate the idea, study the derivation, establish the global
and local convergence, and indicate the efficiency and reliability of the numerical
performance. The book also contains an extensive, not complete,
bibliography which is an important part of the book, and the authors hope
that it will be useful to readers for their further studies.
This book is a result of our teaching experience in various universities
and institutes in China and Brazil in the past ten years. It can be used as a
textbook for an optimization course for graduates and senior undergraduates
in mathematics, computational and applied mathematics, computer science,
operations research, science and engineering. It can also be used as a reference
book for researchers and engineers.
We are indebted to the following colleagues for their encouragement, help,
and suggestions during the preparation of the manuscript: Professors Kang
Feng, Xuchu He, Yuda Hu, Liqun Qi, M.J.D. Powell, Raimundo J.B. Sampaio,
Zhongci Shi, E. Spedicato, J. Stoer, T. Terlaky, and Chengxian Xu.
Special thanks should be given to many of our former students who read
early versions of the book and helped us in improving it. We are grateful
to Edwin F. Beschler and several anonymous referees for many valuable
comments and suggestions. We would like to express our gratitude to the
National Natural Science Foundation of China for the continuous support to
our research. Finally, we are very grateful to Editors John Martindale, Angela
Quilici Burke, and Robert Saley of Springer for their careful and patient
work.
Wenyu Sun, Nanjing Normal University
Yaxiang Yuan, Chinese Academy of Science
April 2005