Author | Kushner, Harold J. author |
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Title | Stochastic Approximation Methods for Constrained and Unconstrained Systems [electronic resource] / by Harold J. Kushner, Dean S. Clark |
Imprint | New York, NY : Springer New York, 1978 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9352-8 |
Descript | X, 263 p. online resource |
I. Introduction -- 1.1. General Remarks -- 1.2. The Robbins-Monro Process -- 1.3. A โContinuousโ Process Version of Section 2 -- 1.4. Regulation of a Dynamical System; a simple example -- 1.5. Function Minimization: The Kiefer-Wolfowitz Procedure -- 1.6. Constrained Problems -- 1.7. An Economics Example -- II. Convergence w.p.1 for Unconstrained Systems -- 2.1. Preliminaries and Motivation -- 2.2. The Robbins-Monro and Kiefer-Wolfowitz Algorithms: Conditions and Discussion -- 2.3. Convergence Proofs for RM and KW-like Procedures -- 2.4. A General Robbins-Monro Process: โExogenous Noiseโ -- 2.5. A General RM Process; State Dependent Noise -- 2.5.1. Extensions and Localizations of Theorem 2.5.2 -- 2.6. Some Applications -- 2.7. Mensov-Rademacher Estimates -- III. Weak Convergence of Probability Measures -- IV. Weak Convergence for Unconstrained Systems -- 4.1. Conditions and General Discussion -- 4.2. The Robbins-Monro and Kiefer-Wolfowitz Procedures -- 4.3. A General Robbins-Monro Process: Exogenous Noise -- 4.4. A General RM Process: State Dependent Noise -- 4.5. The Identification Problem -- 4.6. A Counter-Example to Tightness -- 4.7. Boundedness of {Xn} and Tightness of {Xn(โข)} -- V. Convergence w.p.1 For Constrained Systems -- 5.1. A Penalty-Multiplier Algorithm for Equality Constraints -- 5.2. A Lagrangian Method for Inequality Constraints -- 5.3. A Projection Algorithm -- 5.4. A Penalty-Multiplier Method for Inequality Constraints -- VI. Weak Convergence: Constrained Systems -- 6.1. A Multiplier Type Algorithm for Equality Constraints -- 6.2. The Lagrangian Method -- 6.3. A Projection Algorithm -- 6.4. A Penalty-Multiplier Algorithm for Inequality Constraints -- VII. Rates of Convergence -- 7.1. The Problem Formulation -- 7.2. Conditions and Discussions -- 7.3. Rates of Convergence for Case 1, the KW Algorithm -- 7.4. Discussion of Rates of Convergence for Two KW Algorithms