Large-scale nonlinear optimization

✍ Scribed by Di Pillo G., Roma M. (eds.)

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 307
• Series: Nonconvex Optimization and Its Applications
• Category: Library

✦ Synopsis

This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

✦ Table of Contents

LARGE-SCALE NONLINEAR OPTIMIZATION......Page 1
Half-title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 8
1 Introduction......Page 11
2.1 Framework and discretization......Page 12
2.2 Linear algebra: problems without design variables......Page 14
2.3 Linear algebra: problems with design variables......Page 15
2.5 Interior-point algorithms......Page 16
3.1 Framework......Page 17
3.2 Linear algebra......Page 18
4 Application to Goddard's problem......Page 19
5 Conclusion......Page 20
References......Page 22
1 Introduction......Page 25
2 Proof......Page 30
References......Page 33
1 Introduction......Page 35
2 Generalization of PAV algorithm......Page 37
4 Numerical results......Page 39
References......Page 42
1 Introduction......Page 45
2 Overview of the Package......Page 47
3 Interior-Point Methods......Page 48
3.1 Algorithm I: KNITRO-INTERIOR/DIRECT......Page 49
3.2 Algorithmic Option II: KNITRO-INTERIOR/CG......Page 52
3.3 Merit Function......Page 55
4 Active-set Sequential Linear-Quadratic Programming......Page 56
4.1 Algorithm III: KNITRO-ACTIVE......Page 57
5 Projected CG Iteration......Page 60
6 Special Algorithmic Features......Page 62
7 Crossover......Page 65
References......Page 67
1 Introduction......Page 71
2.1 General considerations......Page 72
2.2 Improved eigenvalue bounds with the reduced-space basis......Page 73
3.1 Structural considerations......Page 80
3.2 Solution considerations......Page 81
3.3 Considerations relating to preconditioning......Page 82
3.4 Particular choices of P and B......Page 83
4 Numerical experiments......Page 85
5 Comments and conclusions......Page 89
References......Page 90
1 Introduction......Page 93
2 Equality constrained problems......Page 95
3 Bound constrained problems......Page 97
4 Bound and equality constrained problems......Page 100
5 Conclusions......Page 101
References......Page 102
1 Introduction......Page 105
2 Separation of polyhedra defined by inequalities......Page 106
3 Separation of polyhedra defined by equations with nonnegative variables......Page 115
4 The thickest separating family of parallel hyperplanes......Page 117
5 The generalized Newton method......Page 122
References......Page 123
1 Introduction......Page 125
2 Exact penalty functions for the GNEP......Page 128
3 Updating the penalty parameters......Page 131
References......Page 135
1 Introduction......Page 137
2 The Reaction-Diffusion Optimal Boundary Control Problem......Page 139
2.1 State Equation and Optimality System......Page 141
2.2 Parameter Dependence......Page 143
3 Properties of the Linearized Problem......Page 145
4 Properties of the Nonlinear Problem......Page 152
5 Numerical Results......Page 153
References......Page 158
1 Introduction......Page 161
2 (R)SQP variants on the structured KKT System......Page 163
3 Pseudo-Newton Solvers and Piggy-backing......Page 166
4 Necessary Convergence Condition on H*......Page 173
5 Numerical Verification......Page 177
6 Summary and Outlook......Page 179
References......Page 181
1 Introduction......Page 183
2 Necessary and sufficient conditions......Page 185
3 Characterizations and parametric representations......Page 189
References......Page 193
1 Introduction......Page 195
2.1 Limited memory BFGS method......Page 196
2.2 Methods based on reduced Hessian matrices......Page 198
2.3 Shifted variable metric methods......Page 199
2.4 Shifted limited-memory variable metric methods......Page 201
3.1 Principles of bundle methods......Page 204
3.2 Variable metric methods for nonsmooth problems......Page 207
3.3 Variable metric methods for large-scale nonsmooth problems......Page 209
3.4 Variable metric methods for partially separable minimax problems......Page 212
4 Hybrid methods for large-scale nonlinear least squares......Page 213
5 Methods for solving large-scale trust-region subproblems......Page 215
References......Page 219
1 Introduction......Page 221
2 The variational model......Page 223
3 An algorithm for VI(c, K f)......Page 225
4 Computational considerations and concluding remarks......Page 228
References......Page 230
Daniele Peri, Antonio Pinto, and Emilio F. Campana......Page 233
2 Description of the GO algorithm......Page 234
3 Multi-Objective Optimisation Test......Page 241
3.1 Selection of the Objective Functions......Page 242
3.2 Hull Shape Modification......Page 244
3.4 Numerical results......Page 245
References......Page 248
1 Introduction......Page 253
2 2D Molten Carbonate Fuel Cell Model......Page 254
3 Simulation Results......Page 259
4 Conclusions......Page 262
References......Page 263
1 Introduction......Page 265
2 An outline of the method......Page 268
3 The initial calculations......Page 272
4 The updating procedures......Page 275
5 The trust region subproblem......Page 282
6 Subroutines BIGLAG and BIGDEN......Page 285
7 Other details of NEWUOA......Page 292
8 Numerical results......Page 296
Appendix: Proofs for Section 3......Page 302
Acknowledgements......Page 306
References......Page 307