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4. Optimization Methods 1. Introduction
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2. Comparing Time Streams of Economic Benefits and Costs 2.1. Interest Rates 82 2.2. Equivalent Present Value 82 2.3. Equivalent Annual Value 82
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3. Non-Linear Optimization Models and Solution Procedures 3.1. Solution Using Calculus 84 3.2. Solution Using Hill Climbing 84 3.3. Solution Using Lagrange Multipliers 86 3.3.1. Approach 86 3.3.2. Meaning of the Lagrange Multiplier 88
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4. Dynamic Programming 90 4.1. Dynamic Programming Networks and Recursive Equations 4.2. Backward-Moving Solution Procedure 92 4.3. Forward-Moving Solution Procedure 95 4.4. Numerical Solutions 96 4.5. Dimensionality 97 4.6. Principle of Optimality 97 4.7. Additional Applications 97 4.7.1. Capacity Expansion 98 4.7.2. Reservoir Operation 102 4.8. General Comments on Dynamic Programming 112
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5. Linear Programming 113 5.1. Reservoir Storage Capacity–Yield Models 114 5.2. A Water Quality Management Problem 117 5.2.1. Model Calibration 118 5.2.2. Management Model 119 5.3. A Groundwater Supply Example 124 5.3.1. A Simplified Model 125 5.3.2. A More Detailed Model 126 5.3.3. An Extended Model 127 5.3.4. Piecewise Linearization Methods 128 5.4. A Review of Linearization Methods 129 6. A Brief Review 7. Reference
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WATER RESOURCES SYSTEMS PLANNING AND MANAGEMENT – ISBN 92-3-103998-9 – © UNESCO 2005