Introduction to sensitivity and stability analysis in nonlinear programming, Volume 165 (Mathematics in Science and Engineering)

✍ Scribed by Fiacco (editor)

• Publisher: Academic Press
• Year: 1983
• Tongue: English
• Leaves: 381
• Category: Library

✦ Table of Contents

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