Continuous optimization: Current trends and modern applications

Contents......Page 6
Preface......Page 13
List of Contributors......Page 14
Part I: Surveys......Page 18
1 Introduction......Page 19
2 Linear semi-infinite systems......Page 21
3 Applications......Page 24
4 Numerical methods......Page 27
5 Perturbation analysis......Page 29
References......Page 33
1 Introduction......Page 39
2 Constrained Interpolation in Hilbert Space......Page 42
3 Nonsmooth Functions and Equations......Page 47
4 Newton\'s Method and Convergence Analysis......Page 49
5 Open Problems......Page 61
References......Page 62
Optimization Methods in Direct and Inverse Scattering......Page 66
1 Introduction......Page 67
2 Identification of small subsurface inclusions......Page 69
3 Identification of layers in multilayer particles......Page 78
4 Potential scattering and the Stability Index method......Page 85
5 Inverse scattering problem with fixed-energy data......Page 95
6 Obstacle scattering by the Modified Rayleigh Conjecture (MRC) method......Page 101
7 Support Function Method for inverse obstacle scattering problems......Page 110
8 Analysis of a Linear Sampling method......Page 117
References......Page 120
1 Introduction......Page 126
2 Complexity of two-stage stochastic programs......Page 129
3 What is easy and what is difficult in stochastic programming?......Page 137
4 Some novel approaches......Page 148
References......Page 159
1 Introduction......Page 162
2 A solver suite approach to practical global optimization......Page 167
3 Modeling systems and user demands......Page 169
4 Software implementation examples......Page 171
6 Conclusions......Page 183
References......Page 184
1 Introduction......Page 189
2 Preliminaries......Page 191
3 Max-min separability......Page 194
4 Minimization of the error function......Page 205
5 Results of numerical experiments......Page 214
6 Conclusions and further work......Page 218
References......Page 219
1 Introduction......Page 222
2 Support functions and lower approximations......Page 223
3 Optimization: the Cutting Angle method......Page 230
4 Random variate generation: acceptance/ rejection......Page 237
5 Scattered data interpolation: Lipschitz approximation......Page 248
References......Page 257
Part II: Theory and Numerical Methods......Page 262
1 Introduction......Page 263
2 Global Optimality Condition......Page 264
3 Approximation Techniques of the Level Set......Page 266
4 Algorithms and their Convergence......Page 274
5 Numerical Examples......Page 282
References......Page 284
1 Introduction......Page 286
2 Monotonicity and convexity......Page 287
3 Monotone optimization and concave minimization......Page 292
4 Polyblock outer approximation method......Page 294
5 A hybrid method......Page 297
6 Conclusions......Page 299
References......Page 300
1 Introduction and Preliminaries......Page 303
2 Generalized Lagrange Multipliers......Page 306
3 Special Cases and Applications......Page 314
4 Directionally Differentiable Problems with DSL-approximates......Page 324
References......Page 327
1 Introduction......Page 330
2 Preliminaries......Page 332
3 A Sum Theorem for Slice Convergence......Page 336
4 Saddle–point Convergence in Fenchel Duality......Page 345
References......Page 350
1 Introduction......Page 351
2 Preliminaries......Page 352
3 Plus-Minkowski gauge and plus-weak Pareto point for a downward set......Page 355
4 X[sub(φ)]-subdifferential of a topical function......Page 357
5 Fenchel-Moreau conjugates with respect to φ......Page 361
6 Conjugate of type Lau with respect to φ......Page 365
References......Page 368
Part III: Applications......Page 370
1 Introduction......Page 371
2 Relationship between two variables: relational elasticity......Page 373
3 Some examples for calculating relational elasticities......Page 375
4 Dynamical systems......Page 376
5 Classification Algorithm based on a dynamical systems approach......Page 380
6 Algorithm for global optimization......Page 383
7 Results of numerical experiments......Page 386
8 Conclusions and future work......Page 387
References......Page 389
1 Introduction......Page 392
2 Single–Rumour Process and Preliminaries......Page 394
3 Scenario 1......Page 396
4 Monotonicity of ξ......Page 400
5 Convexity of ξ......Page 404
6 Scenario 2......Page 407
7 Comparison of Scenarios......Page 410
References......Page 411
1 Introduction......Page 413
2 A class of sum-min functions......Page 414
3 Examples......Page 415
4 Minimization of sum-min functions belonging to class F......Page 419
5 Minimization of generalized cluster function......Page 421
6 Numerical experiments with generalized cluster function......Page 423
7 Skeletons......Page 428
8 Conclusions......Page 434
References......Page 437
1 Introduction......Page 439
2 Problem formulation......Page 440
3 Intuitive calculation of the invariant probability......Page 442
4 Existence of the inverse matrices......Page 444
5 Probabilistic analysis......Page 445
7 Extension of the fundamental ideas......Page 449
References......Page 454