Numerical Optimization

Jorge Nocedal, Stephen Wright

Springer Science & Business Media, Dec 11, 2006 - Mathematics - 664 pages

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

There is a selected solutions manual for instructors for the new edition.

Contents

• 2: 11
• ContinuousversusDiscreteOptimization: 12
• Convergence Rate of Steepest Descent: 42
• QuasiNewton Methods: 89
• StochasticandDeterministicOptimization: 95
• Conjugate Gradient Methods: 101
• Practical Preconditioners: 120
• Global Convergence: 126
• Notes and References: 132
• QuasiNewton Methods: 153
• LargeScale Unconstrained Optimization: 165
• 3: 178
• Exercises: 191
• Vector Functions and Partial Separability: 210
• Current Limitations: 216
• Notes and References: 242
• LeastSquares Problems: 245
• Nonlinear Equations: 274
• 2: 285
• 60: 295
• Exercises: 302
• 2: 307
• 4: 309
• Proof of Theorem 12 1: 329
• Exercises: 349
• The Simplex Method: 355
• 5: 375
• 6: 382
• Notes and References: 389
• InteriorPoint Methods: 392
• Central Path Neighborhoods and PathFollowing Methods: 399
• Notes and References: 416
• 4: 435
• TrustRegion Methods: 437
• 6: 443
• Quadratic Programming: 450
• 1: 476
• The Dogleg Method: 496
• Penalty and Augmented Lagrangian Methods: 497
• 2: 518
• SecondOrder Correction: 543
• 7: 556
• InteriorPoint Methods for Nonlinear Programming: 563
• Updating the Barrier Parameter: 572
• 5: 578
• A Background Material: 598
• B A Regularization Procedure: 635
• 102: 642
• 220: 648
• 305: 652
• Index: 653
• 455: 656
• 2: 659

Bibliographic information

• Title: Numerical Optimization; Springer Series in Operations Research and Financial Engineering; Mathematics and Statistics; Mathematics and Statistics (R0)
• Authors: Jorge Nocedal, Stephen Wright
• Edition: 2, illustrated
• Publisher: Springer Science & Business Media, 2006
• ISBN: 0387400656, 9780387400655
• Length: 664 pages
• Subjects: Business & Economics / General; Business & Economics / Operations Research; Mathematics / General; Mathematics / Numerical Analysis; Mathematics / Optimization; Mathematics / Probability & Statistics / Stochastic Processes; Science / System Theory