Optimization Theory and Methods: Nonlinear Programming

✍ Scribed by Wenyu Sun, Ya-Xiang Yuan (auth.)

• Publisher: Springer US
• Year: 2006
• Tongue: English
• Leaves: 700
• Series: Springer Optimization and Its Applications 1
• Edition: 1
• Category: Library

✦ Synopsis

This book, a result of the authors’ teaching and research experience in various universities and institutes over the past ten years, can be used as a textbook for an optimization course for graduates and senior undergraduates. It systematically describes optimization theory and several powerful methods, including recent results. For most methods, the authors discuss an idea’s motivation, study the derivation, establish the global and local convergence, describe algorithmic steps, and discuss the numerical performance. The book deals with both theory and algorithms of optimization concurrently. It also contains an extensive bibliography with 366 references. Finally, apart from its use for teaching, Optimization Theory and Methods is also very beneficial for doing research.

Audience

This book is intended for senior students, graduates, teachers, and researchers in optimization, operations research, computational mathematics, applied mathematics, and some engineering and economics. It will also be useful for scientists in engineering and economics.

✦ Table of Contents

Introduction....Pages 1-70
Line Search....Pages 71-117
Newton’s Methods....Pages 119-173
Conjugate Gradient Method....Pages 175-201
Quasi-Newton Methods....Pages 203-301
Trust-Region Methods and Conic Model Methods....Pages 303-351
Solving Nonlinear Least-Squares Problems....Pages 353-383
Theory of Constrained Optimization....Pages 385-410
Quadratic Programming....Pages 411-453
Penalty Function Methods....Pages 455-492
Feasible Direction Methods....Pages 493-521
Sequential Quadratic Programming....Pages 523-560
Trust-Region Methods for Constrained Problems....Pages 561-595
Nonsmooth Optimization....Pages 597-635

✦ Subjects

Optimization; Numerical Analysis; Operations Research, Mathematical Programming; Computational Science and Engineering