UID:
almafu_9958099630302883
Umfang:
1 online resource (381 p.)
ISBN:
1-282-28963-2
,
9786612289637
,
0-08-095671-8
Serie:
Mathematics in science and engineering ; v. 165
Inhalt:
Introduction to sensitivity and stability analysis in nonlinear programming
Anmerkung:
Description based upon print version of record.
,
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
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3.1 Introduction3.2 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
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5.3 Examples of Early Sensitivity Interpretations of Lagrange Multipliers5.4 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
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6.4 Extensions6.5 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
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7.4 Sensitivity Results for Augmented Lagrangians7.5 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
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9.2 Computable Piecewise Linear Upper and Lower Optimal Value Bounds
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English
Weitere Ausg.:
ISBN 0-12-254450-1
Sprache:
Englisch
Fachgebiete:
Mathematik
URL:
Volltext
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