Practical Methods of Optimization (2 SUB)

Practical Methods of Optimization (2 SUB)

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  • 製本 Hardcover:ハードカバー版
  • 言語 ENG,ENG
  • 商品コード 9780471915478
  • DDC分類 515

Table of Contents

Preface                                            ix
Table of Notation xiii
PART 1 UNCONSTRAINED OPTIMIZATION 1 (136)
Introduction 3 (9)
History and Applications 3 (3)
Mathematical Background 6 (6)
Questions for Chapter 1 11 (1)
Structure of Methods 12 (32)
Conditions for Local Minima 12 (4)
Ad hoc Methods 16 (3)
Useful Algorithmic Properties 19 (5)
Quadratic Models 24 (2)
Descent Methods and Stability 26 (7)
Algorithms for the Line Search Subproblem 33 (11)
Questions for Chapter 2 40 (4)
Newton-like Methods 44 (36)
Newton's Method 44 (5)
Quasi-Newton Methods 49 (8)
Invariance, Metrics and Variational 57 (5)
Properties
The Broyden Family 62 (6)
Numerical Experiments 68 (4)
Other Formulae 72 (8)
Questions for Chapter 3 74 (6)
Conjugate Direction Methods 80 (15)
Conjugate Gradient Methods 80 (7)
Direction Set Methods 87 (8)
Questions for Chapter 4 92 (3)
Restricted Step Methods 95 (15)
A Prototype Algorithm 95 (5)
Levenberg-Marquardt Methods 100 (10)
Questions for Chapter 5 108 (2)
Sums of Squares and Nonlinear Equations 110 (27)
Over-determined Systems 110 (9)
Well-determined Systems 119 (10)
No-derivative Methods 129 (8)
Questions for Chapter 6 133 (4)
PART 2 CONSTRAINED OPTIMIZATION 137 (280)
Introduction 139 (11)
Preview 139 (5)
Elimination and Other Transformations 144 (6)
Questions for Chapter 7 149 (1)
Linear Programming 150 (45)
Structure 150 (3)
The Simplex Method 153 (6)
Other LP Techniques 159 (3)
Feasible Points for Linear Constraints 162 (6)
Stable and Large-scale Linear Programming 168 (9)
Degeneracy 177 (6)
Polynomial Time Algorithms 183 (12)
Questions for Chapter 8 188 (7)
The Theory of Constrained Optimization 195 (34)
Lagrange Multipliers 195 (6)
First Order Conditions 201 (6)
Second Order Conditions 207 (6)
Convexity 213 (6)
Duality 219 (10)
Questions for Chapter 9 224 (5)
Quadratic Programming 229 (30)
Equality Constraints 229 (7)
Lagrangian Methods 236 (4)
Active Set Methods 240 (5)
Advanced Features 245 (2)
Special QP Problems 247 (3)
Complementary Pivoting and Other Methods 250 (9)
Questions for Chapter 10 255 (4)
General Linearly Constrained Optimization 259 (18)
Equality Constraints 259 (5)
Inequality Constraints 264 (4)
Zigzagging 268 (9)
Questions for Chapter 11 275 (2)
Nonlinear Programming 277 (54)
Penalty and Barrier Functions 277 (10)
Multiplier Penalty Functions 287 (9)
The L1 Exact Penalty Function 296 (8)
The Lagrange-Newton Method (SQP) 304 (13)
Nonlinear Elimination and Feasible 317 (5)
Direction Methods
Other Methods 322 (9)
Questions for Chapter 12 325 (6)
Other Optimization Problems 331 (26)
Integer Programming 331 (8)
Geometric Programming 339 (5)
Network Programming 344 (13)
Questions for Chapter 13 354 (3)
Non-Smooth Optimization 357 (60)
Introduction 357 (7)
Optimality Conditions 364 (14)
Exact Penalty Functions 378 (4)
Algorithms 382 (15)
A Globally Convergent Prototype Algorithm 397 (5)
Constrained Non-Smooth Optimization 402 (15)
Questions for Chapter 14 414 (3)
References 417 (13)
Subject Index 430