Nonlinear programming:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Place of publication not identified]
E-Content Generic Vendor
2014
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| Schriftenreihe: | De Gruyter textbook
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Preface; Notations; 1 Introduction; 1.1 The model; 1.2 Special cases and applications; 1.2.1 Separable problem; 1.2.2 Problem of quadratic optimization; 1.2.3 Further examples of practical applications; 1.3 Complications caused by nonlinearity; 1.4 References for Chapter 1; Part I Theoretical foundations; 2 Optimality conditions; 2.1 Feasible directions; 2.2 First and second-order optimality conditions; 3 The convex optimization problem; 3.1 Convex sets; 3.2 Convex and concave functions; 3.3 Differentiable convex functions; 3.4 Subgradient and directional derivative 3.5 Minima of convex and concave functions4 Karush-Kuhn-Tucker conditions and duality; 4.1 Karush-Kuhn-Tucker conditions; 4.2 Lagrange function and duality; 4.3 The Wolfe dual problem; 4.4 Second-order optimality criteria; 4.5 References for Part I; Part II Solution methods; 5 Iterative procedures and evaluation criteria; 6 Unidimensional minimization; 6.1 Delimitation of the search region; 6.2 Newton's method; 6.3 Interpolation methods; 6.4 On the use of the methods in practice; 7 Unrestricted minimization; 7.1 Analysis of quadratic functions; 7.2 The gradient method 7.3 Multidimensional Newton's method7.4 Conjugate directions and quasi-Newton methods; 7.5 Cyclic coordinate search techniques; 7.6 Inexact line search; 7.7 Trust region methods; 8 Linearly constrained problems; 8.1 Feasible direction methods; 8.1.1 Rosen's gradient projection method; 8.1.2 Zoutendijk's method; 8.1.3 Advanced techniques: an outline; 8.2 Linear equality constraints; 9 Quadratic problems; 9.1 An active-set method; 9.2 Karush-Kuhn-Tucker conditions; 9.3 Lemke's method; 10 The general problem; 10.1 The penalty method; 10.2 The barrier method; 10.3 Sequential quadratic programming 11 Nondifferentiable and global optimization11.1 Nondifferentiable optimization; 11.1.1 Examples for nondifferentiable problems; 11.1.2 Basic ideas of resolution; 11.1.3 The concept of bundle methods; 11.2 Global optimization; 11.2.1 Specific cases of global optimization; 11.2.2 Exact methods; 11.2.3 Heuristic methods; 11.3 References and software for Part II; Appendix: Solutions of exercises; References; Index This book is an introduction to nonlinear programming, written for students from the fields of applied mathematics, engineering, and economy. It deals with theoretical foundations as well assolution methods, beginning with the classical procedures and reaching up to "modern" methods. Several examples, exercises with detailed solutions and applications are provided, making the text adequate for individual studies |
| ISBN: | 3110315289 9783110315288 |
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| 500 | |a Preface; Notations; 1 Introduction; 1.1 The model; 1.2 Special cases and applications; 1.2.1 Separable problem; 1.2.2 Problem of quadratic optimization; 1.2.3 Further examples of practical applications; 1.3 Complications caused by nonlinearity; 1.4 References for Chapter 1; Part I Theoretical foundations; 2 Optimality conditions; 2.1 Feasible directions; 2.2 First and second-order optimality conditions; 3 The convex optimization problem; 3.1 Convex sets; 3.2 Convex and concave functions; 3.3 Differentiable convex functions; 3.4 Subgradient and directional derivative | ||
| 500 | |a 3.5 Minima of convex and concave functions4 Karush-Kuhn-Tucker conditions and duality; 4.1 Karush-Kuhn-Tucker conditions; 4.2 Lagrange function and duality; 4.3 The Wolfe dual problem; 4.4 Second-order optimality criteria; 4.5 References for Part I; Part II Solution methods; 5 Iterative procedures and evaluation criteria; 6 Unidimensional minimization; 6.1 Delimitation of the search region; 6.2 Newton's method; 6.3 Interpolation methods; 6.4 On the use of the methods in practice; 7 Unrestricted minimization; 7.1 Analysis of quadratic functions; 7.2 The gradient method | ||
| 500 | |a 7.3 Multidimensional Newton's method7.4 Conjugate directions and quasi-Newton methods; 7.5 Cyclic coordinate search techniques; 7.6 Inexact line search; 7.7 Trust region methods; 8 Linearly constrained problems; 8.1 Feasible direction methods; 8.1.1 Rosen's gradient projection method; 8.1.2 Zoutendijk's method; 8.1.3 Advanced techniques: an outline; 8.2 Linear equality constraints; 9 Quadratic problems; 9.1 An active-set method; 9.2 Karush-Kuhn-Tucker conditions; 9.3 Lemke's method; 10 The general problem; 10.1 The penalty method; 10.2 The barrier method; 10.3 Sequential quadratic programming | ||
| 500 | |a 11 Nondifferentiable and global optimization11.1 Nondifferentiable optimization; 11.1.1 Examples for nondifferentiable problems; 11.1.2 Basic ideas of resolution; 11.1.3 The concept of bundle methods; 11.2 Global optimization; 11.2.1 Specific cases of global optimization; 11.2.2 Exact methods; 11.2.3 Heuristic methods; 11.3 References and software for Part II; Appendix: Solutions of exercises; References; Index | ||
| 500 | |a This book is an introduction to nonlinear programming, written for students from the fields of applied mathematics, engineering, and economy. It deals with theoretical foundations as well assolution methods, beginning with the classical procedures and reaching up to "modern" methods. Several examples, exercises with detailed solutions and applications are provided, making the text adequate for individual studies | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Peter Zornig |
| author_facet | Peter Zornig |
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| author_sort | Peter Zornig |
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| bvnumber | BV043960724 |
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| dewey-full | 519.76 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.76 |
| dewey-search | 519.76 |
| dewey-sort | 3519.76 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| isbn | 3110315289 9783110315288 |
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| spelling | Peter Zornig Verfasser aut Nonlinear programming [Place of publication not identified] E-Content Generic Vendor 2014 txt rdacontent c rdamedia cr rdacarrier De Gruyter textbook Preface; Notations; 1 Introduction; 1.1 The model; 1.2 Special cases and applications; 1.2.1 Separable problem; 1.2.2 Problem of quadratic optimization; 1.2.3 Further examples of practical applications; 1.3 Complications caused by nonlinearity; 1.4 References for Chapter 1; Part I Theoretical foundations; 2 Optimality conditions; 2.1 Feasible directions; 2.2 First and second-order optimality conditions; 3 The convex optimization problem; 3.1 Convex sets; 3.2 Convex and concave functions; 3.3 Differentiable convex functions; 3.4 Subgradient and directional derivative 3.5 Minima of convex and concave functions4 Karush-Kuhn-Tucker conditions and duality; 4.1 Karush-Kuhn-Tucker conditions; 4.2 Lagrange function and duality; 4.3 The Wolfe dual problem; 4.4 Second-order optimality criteria; 4.5 References for Part I; Part II Solution methods; 5 Iterative procedures and evaluation criteria; 6 Unidimensional minimization; 6.1 Delimitation of the search region; 6.2 Newton's method; 6.3 Interpolation methods; 6.4 On the use of the methods in practice; 7 Unrestricted minimization; 7.1 Analysis of quadratic functions; 7.2 The gradient method 7.3 Multidimensional Newton's method7.4 Conjugate directions and quasi-Newton methods; 7.5 Cyclic coordinate search techniques; 7.6 Inexact line search; 7.7 Trust region methods; 8 Linearly constrained problems; 8.1 Feasible direction methods; 8.1.1 Rosen's gradient projection method; 8.1.2 Zoutendijk's method; 8.1.3 Advanced techniques: an outline; 8.2 Linear equality constraints; 9 Quadratic problems; 9.1 An active-set method; 9.2 Karush-Kuhn-Tucker conditions; 9.3 Lemke's method; 10 The general problem; 10.1 The penalty method; 10.2 The barrier method; 10.3 Sequential quadratic programming 11 Nondifferentiable and global optimization11.1 Nondifferentiable optimization; 11.1.1 Examples for nondifferentiable problems; 11.1.2 Basic ideas of resolution; 11.1.3 The concept of bundle methods; 11.2 Global optimization; 11.2.1 Specific cases of global optimization; 11.2.2 Exact methods; 11.2.3 Heuristic methods; 11.3 References and software for Part II; Appendix: Solutions of exercises; References; Index This book is an introduction to nonlinear programming, written for students from the fields of applied mathematics, engineering, and economy. It deals with theoretical foundations as well assolution methods, beginning with the classical procedures and reaching up to "modern" methods. Several examples, exercises with detailed solutions and applications are provided, making the text adequate for individual studies Linear programming Nonlinear programming / Textbooks MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Nonlinear programming fast Nonlinear programming Textbooks Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s 1\p DE-604 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Peter Zornig Nonlinear programming Linear programming Nonlinear programming / Textbooks Nonlinear programming MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Nonlinear programming fast Nonlinear programming Textbooks Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Nonlinear programming |
| title_auth | Nonlinear programming |
| title_exact_search | Nonlinear programming |
| title_full | Nonlinear programming |
| title_fullStr | Nonlinear programming |
| title_full_unstemmed | Nonlinear programming |
| title_short | Nonlinear programming |
| title_sort | nonlinear programming |
| topic | Linear programming Nonlinear programming / Textbooks Nonlinear programming MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Nonlinear programming fast Nonlinear programming Textbooks Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Linear programming Nonlinear programming / Textbooks Nonlinear programming MATHEMATICS / Applied MATHEMATICS / Probability & Statistics / General Nonlinear programming Textbooks Nichtlineare Optimierung |
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