I. Introduction. - 1. 1. General Remarks. - 1. 2. The Robbins-Monro Process. - 1. 3. A Continuous 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: Exogenous Noise. - 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()}. - 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 1the KW Algorithm. - 7. 4. Discussion of Rates of Convergence for Two KW Algorithms. Language: English