Optimization in Engineering Sciences

Optimization in Engineering Sciences......Page 2
Copyright......Page 3
Table of Contents......Page 4
Foreword......Page 8
Preface......Page 10
Acronyms......Page 12
1.2. Stating the problem......Page 14
1.3. Lagrange method......Page 17
1.4.2. Simplicial form formulation......Page 18
1.4.3. Transition from one simplicial form to another......Page 20
1.4.4. Summary of the simplex algorithm......Page 22
1.5. Implementation example......Page 24
1.6.2. Resource allocation for advertising......Page 26
1.6.3. Optimization of a cut of paper rolls......Page 29
1.6.4. Structure of linear program of an optimal control problem......Page 30
2.1. Problem formulation......Page 35
2.2. Karush?Kuhn?Tucker conditions......Page 36
2.3.1. Main steps......Page 38
2.3.2. Computing the search direction......Page 41
2.4. Monovariable methods......Page 45
2.4.1. Coggin’s method of polynomial interpolation......Page 46
2.4.2. Golden section method......Page 48
2.5.1. Direct search methods......Page 51
2.5.2. Gradient methods......Page 69
3.1.2. Decision problem......Page 113
3.2. Recurrence equation of optimality......Page 114
3.3.3. Random horizon problem......Page 116
3.3.4. Taking into account sum-like constraints......Page 117
3.3.6. Initialization when the final state is imposed......Page 118
3.4.1. Route optimization......Page 119
3.4.2. The smuggler problem......Page 121
4.1. Structure......Page 127
4.2.1. General problem......Page 129
4.2.2. Application to the traveling salesman problem......Page 133
4.3.1. Deterministic method......Page 135
4.3.2. Stochastic method......Page 137
5.1. The optimal identification principle......Page 142
5.2.1. General problem......Page 143
5.2.2. Formulation based on optimization theory......Page 144
5.2.3. Formulation based on estimation theory statistics......Page 147
5.3.1. General model......Page 149
5.3.2. Rational input/output RIO models......Page 151
5.3.3. Class of autoregressive models ARMAX......Page 153
5.3.4. Class of state space representation models......Page 156
5.4.1. LSM type solution......Page 157
5.4.2. Geometric interpretation of the LSM solution......Page 162
5.4.3. Consistency of the LSM type solution......Page 165
5.4.4. Example of application of the LSM for an ARX model......Page 168
5.5.1. Recovering lost consistency......Page 169
5.5.2. Extended LSM......Page 173
5.5.3. Instrumental variables method......Page 175
5.6.1. Basic principle and algorithm......Page 179
5.6.2. Implementation of the MPEM for ARMAX models......Page 182
5.6.3. Convergence and consistency of MPEM type estimations......Page 185
5.7.1. Accuracy/adaptability paradigm......Page 186
5.7.2. Basic adaptive version of the LSM......Page 188
5.7.3. Basic adaptive version of the IVM......Page 193
5.7.4. Adaptive window versions of the LSM and IVM......Page 194
6.1.1. Variation of a functional......Page 202
6.1.2. Constraint-free minimization......Page 203
6.1.3. Hamilton canonical equations......Page 205
6.1.5. Minimization with constraints......Page 206
6.2.1. Formulation......Page 207
6.2.2. Examples of implementation......Page 209
6.3. Maximum principle, discrete case......Page 217
6.4. Principle of optimal command based on quadratic criteria......Page 218
6.5.1. Finite horizon LQ command......Page 221
6.5.2. The infinite horizon QL command......Page 228
6.5.3. Robustness of the LQ command......Page 232
6.6. Optimal filtering......Page 235
6.6.1. Kalman?Bucy predictor......Page 236
6.6.2. Kalman?Bucy filter......Page 242
6.6.3. Stability of Kalman?Bucy estimators......Page 245
6.6.4. Robustness of Kalman?Bucy estimators......Page 246
6.7. Design of the LQG command......Page 250
6.8.1. Optimal control by state fee......Page 256
6.8.2. Quadratic stabilization......Page 259
6.8.3. Optimal command based on output feedback......Page 260
7.1. Characteristics of complex optimization problems......Page 262
7.2. Decomposition techniques......Page 263
7.2.1. Problems with block-diagonal structure......Page 264
7.2.2. Problems with separable criteria and constraints......Page 278
7.3. Penalization techniques......Page 294
7.3.1. External penalization technique......Page 295
7.3.2. Internal penalization technique......Page 296
7.3.3. Extended penalization technique......Page 297
8.1. Introduction......Page 299
8.2. Factors influencing the construction of IT systems......Page 300
8.3. Approaches......Page 302
8.4. Selection of computing tools......Page 306
8.6. Evaluation......Page 307
8.7. Conclusions......Page 308
Bibliography......Page 309
Index......Page 316