Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
Published on 14. May 2014
381 pages
978-0-08-095671-8 (ISBN)
Description
Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095671-8 (9780080956718)
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Schweitzer Classification
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Additional editions
Book
11/1997
Academic Press
€81.71
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Content
- Front Cover
- Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
- Copyright Page
- Contents
- Preface
- PART I: Overview
- Chapter 1. Motivation and Perspective
- Chapter 2. Basic Sensitivity and Stability Results
- 2.1 Introduction
- 2.2 Objective Function and Solution Set Continuity
- 2.3 Differential Stability
- 2.4 Implicit Function Theorem Results
- 2.5 Optimal Value and Solution Bounds
- 2.6 General Results from RHS Results
- 2.7 Summary
- PART II: Theory and Calculation of Solution Parameter Derivatives
- Chapter 3. Sensitivity Analysis under Second- Order Assumptions
- 3.1 Introduction
- 3.2 First-Order Sensitivity Analysis of a Second-Order Local Solution
- 3.3 Examples
- 3.4 First- and Second-Order Parameter Derivatives of the Optimal Value Function
- Chapter 4. Computational Aspects of Sensitivity Calculations: The General Problem
- 4.1 Introduction
- 4.2 Formulas for the Parameter First Derivatives of a Karush-Kuhn-Tucker Triple
- 4.3 Applications and Examples
- Chapter 5. Computational Aspects: RHS Perturbations
- 5.1 Introduction
- 5.2 The Use and Initial Interpretation of Lagrange Multipliers
- 5.3 Examples of Early Sensitivity Interpretations of Lagrange Multipliers
- 5.4 Supporting Theory
- 5.5 Formulas for the Parameter First Derivatives of a Karush-Kuhn-Tucker Triple and Second Derivatives of the Optimal Value Function
- 5.6 Examples and Applications
- PART III: Algorithmic Approximations
- Chapter 6. Estimates of Sensitivity Information Using Penalty Functions
- 6.1 Introduction
- 6.2 Approximation of Sensitivity Information Using the Logarithmic- Quadratic Mixed Barrier-Penalty Function Method
- 6.3 Examples of Estimates of Solution Point and Lagrange Multiplier Parameter Derivatives
- 6.4 Extensions
- 6.5 Sensitivity Calculations Based on the Perturbed Karush-Kuhn-Tucker System
- 6.6 Optimal Value Function Sensitivity Estimates
- 6.7 Example of Estimates of Optimal Value and First- and Second- Parameter Derivatives
- 6.8 Sensitivity Approximations for RHS Perturbations
- 6.9 Recapitulation
- Chapter 7. Calculation of Sensitivity Information Using Other Algorithms
- 7.1 Introduction
- 7.2 Connections between Algorithmic and Sensitivity Calculations
- 7.3 Algorithmic Calculations of the Inverse of the Jacobian of the Karush-Kuhn-Tucker System
- 7.4 Sensitivity Results for Augmented Lagrangians
- 7.5 Conclusions and Extensions
- PART IV: Applications and Future Research
- Chapter 8. An Example of Computational Implementations: A Multi-Item Continuous Review Inventory Model
- 8.1 Introduction
- 8.2 Screening of Sensitivity Information
- 8.3 Example Sensitivity Calculations by SENSUMT
- 8.4 A Multi-Item Inventory Model
- 8.5 Additional Computational Experience with Applications
- Chapter 9. Computable Optimal Value Bounds and Solution Vector Estimates for Parametric NLP Programs
- 9.1 Introduction
- 9.2 Computable Piecewise Linear Upper and Lower Optimal Value Bounds
- 9.3 Estimates of a Parametric Solution Vector and a Sharper Convex Upper Bound
- 9.4 Connections between Optimal Value Bounds and Duality
- 9.5 Nonlinear Dual Lower Bounds
- 9.6 Extensions
- 9.7 Bounds on a Solution Point
- 9.8 Further Extensions and Applications
- Chapter 10. Future Research and Applications
- 10.1 Recapitulation and Other Research Directions
- 10.2 Future Research Directions and Applications
- 10.3 Conclusions
- Appendix I: Notation, Conventions, and Symbols
- Appendix II: Lemmas, Theorems, Corollaries, Definitions, and Examples
- References
- Selected Bibliography of Works Not Cited
- Author Index
- Subject Index
