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Pt. I Basic Stochastic Optimization Methods
1 Decision/Control Under Stochastic Uncertainty 3
2 Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty 9
Pt. II Differentiation Methods
3 Differentiation Methods for Probability and Risk Functions 43
Pt. III Deterministic Descent Directions
4 Deterministic Descent Directions and Efficient Points 95
Pt. IV Semi-Stochastic Approximation Methods
5 RSM-Based Stochastic Gradient Procedures 129
6 Stochastic Approximation Methods with Changing Error Variances 177
Pt. V Reliability Analysis of Structures/Systems
7 Computation of Probabilities of Survival/Failure by Means of Piecewise Linearization of the State Function 253
Pt. VI Appendix
A Sequences, Series and Products 301
B Convergence Theorems for Stochastic Sequences 313
C Tools from Matrix Calculus 321
References 327
Index 335
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