BONUS Algorithm for Large Scale Stochastic Nonlinear Programming Problems

Cover
SpringerBriefs in Optimization
BONUS Algorithm for Large Scale Stochastic Nonlinear Programming Problems
Copyright
     © Urmila Diwekar; Amy David 2015
     ISSN 2190-8354
     ISSN 2191-575X (electronic)
     ISBN 978-1-4939-2281-9
     ISBN 978-1-4939-2282-6 (eBook)
     DOI 10.1007/978-1-4939-2282-6
     Library of Congress Control Number: 2014955715
Preface
Contents
List of Figures
List of Tables

Chapter 1 Introduction
     1.1 Stochastic Optimization Problems
     1.2 Stochastic Nonlinear Programming
     1.3 Summary
     Notations

Chapter 2 Uncertainty Analysis and Sampling Techniques
     2.1 Specifying Uncertainty Using Probability Distributions
     2.2 Sampling Techniques
          2.2.1 Monte Carlo Sampling
     2.3 Variance Reduction Techniques
          2.3.1 Importance Sampling
          2.3.2 Stratified Sampling
          2.3.3 Quasi-Monte Carlo Methods
     2.4 Summary
     Notations

Chapter 3 Probability Density Functions and Kernel Density Estimation
     3.1 The Histogram
     3.2 Kernel Density Estimator
     3.3 Summary
     Notations

Chapter 4 The BONUS Algorithm
     4.1 Reweighting Schemes
     4.2 Effect of Sampling on Reweighting
     4.3 BONUS: The Novel SNLP Algorithm
     4.4 Summary
     Notations

Chapter 5 Water Management Under Weather Uncertainty
     5.1 Introduction
     5.2 The Pulverized Coal Power Plant
     5.3 Parameter Uncertainty
     5.4 Problem Formulation
     5.5 Selection of Decision Variables
     5.6 Implementation of BONUS Algorithm
     5.7 Results
     5.8 Summary
     Notations

Chapter 6 Real-Time Optimization for Water Management
     6.1 Introduction
     6.2 Power Plant Operations
     6.3 Formulation of the Stochastic Problem
     6.4 Solution Approach
     6.5 Weather Forecasting and Uncertainty Quantification
          6.5.1 Ensemble Initialization
          6.5.2 Ensemble Propagation
          6.5.3 Validation of Weather Forecast
     6.6 Application to Pulverized Coal Power Plant
     6.7 Summary
     Notations

Chapter 7 Sensor Placement Under Uncertainty for Power Plants
     7.1 Introduction
          7.1.1 The Integrated Gasification Combined Cycle Power Plant
          7.1.2 Measurement Uncertainty
     7.2 Fisher Information and Its Use in the Sensor-Placement Problem
     7.3 Computation of Fisher Information
          7.3.1 Reweighting Using the BONUS Method
          7.3.2 Calculating the Fisher Information from Kernel Density Estimation
     7.4 The Optimization Problem
          7.4.1 Defining the Objective Function
          7.4.2 The IGCC Power Plant
          7.4.3 Problem Approach
          7.4.4 Results
     7.5 Summary
     Notations

Chapter 8 The L-Shaped BONUS Algorithm
     8.1 The L-Shaped BONUS Algorithm
     8.2 Illustrative Example 1: The Farmer\'s Problem
          8.2.1 Problem Formulation
          8.2.2 Problem Solution
          8.2.3 Results of the Farmer\'s Problem
     8.3 Illustrative Example 2: The Blending Problem
          8.3.1 Problem Formulation
          8.3.2 Simulations and Results
     8.4 Summary
     Notations

Chapter 9 The Environmental Trading Problem
     9.1 Introduction
     9.2 Basics of Pollutant Trading
     9.3 Christina Watershed Nutrient Management
     9.4 Trading Problem Formulation
     9.5 Results
     9.6 Summary
     Notations

Chapter 10 Water Security Networks
     10.1 Introduction
     10.2 Motivation and Prior Work
     10.3 Solution Methodology
          10.3.1 Use of BONUS Reweighting for Pattern Estimation
          10.3.2 Back Estimation of Flow Patterns
     10.4 Results
     10.5 Summary
     Notations

References

Index