Introduction to sensitivity and stability analysis in nonlinear programming /:
Introduction to sensitivity and stability analysis in nonlinear programming.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1983.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 165. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | Introduction to sensitivity and stability analysis in nonlinear programming. |
| Beschreibung: | 1 online resource (xii, 367 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9780122544507 0122544501 9780080956718 0080956718 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to sensitivity and stability analysis in nonlinear programming / |c Anthony V. Fiacco. |
| 260 | |a New York : |b Academic Press, |c 1983. | ||
| 300 | |a 1 online resource (xii, 367 pages) | ||
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| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
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| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a Introduction to sensitivity and stability analysis in nonlinear programming. | ||
| 650 | 0 | |a Nonlinear programming. |0 http://id.loc.gov/authorities/subjects/sh85092331 | |
| 650 | 6 | |a Programmation non linéaire. | |
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| 653 | |a Nonlinear programming | ||
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Datensatz im Suchindex
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|---|---|
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| adam_text | |
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| author | Fiacco, Anthony V. |
| author_facet | Fiacco, Anthony V. |
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| author_variant | a v f av avf |
| building | Verbundindex |
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| callnumber-search | T57.8 .F53 1983eb |
| callnumber-sort | T 257.8 F53 41983EB |
| callnumber-subject | T - General Technology |
| collection | ZDB-4-EBA |
| 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 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 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 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 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 |
| ctrlnum | (OCoLC)316568494 |
| dewey-full | 519.7/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/6 |
| dewey-search | 519.7/6 |
| dewey-sort | 3519.7 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn316568494 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
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| isbn | 9780122544507 0122544501 9780080956718 0080956718 |
| language | English |
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| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 367 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Academic Press, |
| record_format | marc |
| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Fiacco, Anthony V. Introduction to sensitivity and stability analysis in nonlinear programming / Anthony V. Fiacco. New York : Academic Press, 1983. 1 online resource (xii, 367 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 165 Includes bibliographical references and indexes. Print version record. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL 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 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 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 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 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 Introduction to sensitivity and stability analysis in nonlinear programming. Nonlinear programming. http://id.loc.gov/authorities/subjects/sh85092331 Programmation non linéaire. MATHEMATICS Linear & Nonlinear Programming. bisacsh Nonlinear programming fast Nonlinear programming Print version: Fiacco, Anthony V. Introduction to sensitivity and stability analysis in nonlinear programming. New York : Academic Press, 1983 9780122544507 (DLC) 82011642 (OCoLC)8667936 Mathematics in science and engineering ; v. 165. http://id.loc.gov/authorities/names/n42015986 FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/165 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297027 Volltext |
| spellingShingle | Fiacco, Anthony V. Introduction to sensitivity and stability analysis in nonlinear programming / Mathematics in science and engineering ; 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 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 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 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 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 Nonlinear programming. http://id.loc.gov/authorities/subjects/sh85092331 Programmation non linéaire. MATHEMATICS Linear & Nonlinear Programming. bisacsh Nonlinear programming fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85092331 |
| title | Introduction to sensitivity and stability analysis in nonlinear programming / |
| title_auth | Introduction to sensitivity and stability analysis in nonlinear programming / |
| title_exact_search | Introduction to sensitivity and stability analysis in nonlinear programming / |
| title_full | Introduction to sensitivity and stability analysis in nonlinear programming / Anthony V. Fiacco. |
| title_fullStr | Introduction to sensitivity and stability analysis in nonlinear programming / Anthony V. Fiacco. |
| title_full_unstemmed | Introduction to sensitivity and stability analysis in nonlinear programming / Anthony V. Fiacco. |
| title_short | Introduction to sensitivity and stability analysis in nonlinear programming / |
| title_sort | introduction to sensitivity and stability analysis in nonlinear programming |
| topic | Nonlinear programming. http://id.loc.gov/authorities/subjects/sh85092331 Programmation non linéaire. MATHEMATICS Linear & Nonlinear Programming. bisacsh Nonlinear programming fast |
| topic_facet | Nonlinear programming. Programmation non linéaire. MATHEMATICS Linear & Nonlinear Programming. Nonlinear programming |
| url | https://www.sciencedirect.com/science/bookseries/00765392/165 https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297027 |
| work_keys_str_mv | AT fiaccoanthonyv introductiontosensitivityandstabilityanalysisinnonlinearprogramming |