Numerical optimization. Theoretical and practical aspects

✍ Scribed by Bonnans J.F., Gilbert J.C., et al.

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 490
• Series: Universitext
• Category: Library

✦ Synopsis

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition of Numerical Optimization contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.

✦ Table of Contents

Title......Page 1
Preface......Page 3
Table of Contents......Page 5
1 General Introduction......Page 14
2 Basic Methods......Page 34
3 Line-Searches......Page 45
4 Newtonian Methods......Page 59
5 Conjugate Gradient......Page 75
6 Special Methods......Page 85
7 A Case Study: Seismic Reection Tomography......Page 105
8 Introduction to Nonsmooth Optimization......Page 115
9 Some Methods in Nonsmooth Optimization......Page 125
10 Bundle Methods. The Quest for Descent......Page 143
11 Applications of Nonsmooth Optimization......Page 166
12 Computational Exercises......Page 188
13 Background......Page 201
14 Local Methods for Problems with Equality Constraints......Page 219
15 Local Methods for Problems with Equality and Inequality Constraints......Page 258
16 Exact Penalization......Page 274
17 Globalization by Line-Search......Page 291
18 Quasi-Newton Versions......Page 325
19 Linearly Constrained Optimizationand Simplex Algorithm......Page 353
20 Linear Monotone Complementarityand Associated Vector Fields......Page 370
21 Predictor-Corrector Algorithms......Page 394
22 Non-Feasible Algorithms......Page 409
23 Self-Duality......Page 422
24 One-Step Methods......Page 432
25 Complexity of Linear OptimizationProblems with Integer Data......Page 448
26 Karmarkar's Algorithm......Page 454
References......Page 461
Index......Page 481