Nonlinear optimization: methods and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2019]
|
| Schriftenreihe: | International series in operations research & management science
volume 282 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 366 Seiten Illustrationen |
| ISBN: | 9783030194611 |
Internformat
MARC
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| 245 | 1 | 0 | |a Nonlinear optimization |b methods and applications |c H. A. Eiselt, Carl-Louis Sandblom |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents 1 Introduction.................................................................................................... 1.1 The Nonlinear Programming Problem............................................... 1.2 Necessary and Sufficient Conditions for Local Minima.................. 1.3 Convex Functions and Quadratic Forms........................................... References........................................................................................................ 1 1 3 16 23 2 Unconstrained Optimization....................................................................... 2.1 Single-Variable Unconstrained Optimization................................... 2.1.1 Grid Search.............................................................................. 2.1.2 Dichotomous Search............................................................... 2.1.3 Bisection Search...................................................................... 2.1.4 Fibonacci Search..................................................................... 2.1.5 Golden Section Search........................................................... 2.1.6 Quadratic Interpolation........................................................... 2.1.7 Cubic Interpolation................................................................. 2.1.8 Newton Minimization Search................................................ 2.1.9 Lipschitz Optimization........................................................... 2.2 Multiple-Variable Unconstrained Optimization................................ 2.2.1 Cyclic Coordinate Descent and
Simplex Search................. 2.2.2 The Gradient (Steepest Descent) Method............................. 2.2.3 Inexact Line Searches............................................................. 2.2.4 The Davidon-Fletcher-Powell Method................................ 2.2.5 The Fletcher-Reeves Conjugate Gradient Method.............. 2.2.6 The BFGS Method.................................................................. 2.2.7 The Newton Minimization Method....................................... 2.2.8 Trust Region Methods............................................................ References........................................................................................................ 25 25 26 27 28 30 35 37 38 41 46 49 50 52 56 59 62 64 66 69 75 3 Applications of Nonlinear Programming.................................................. 3.1 Curve Fitting........................................................................................ 3.2 Reference Point Programming with EuclideanDistances................ 77 78 83
viii Contents 3.3 Optimal Rotation Time in Forestry.................................................... 3.4 Queuing Optimization......................................................................... 3.5 Portfolio Selection Analysis............................................................... 3.6 Optimizing an Electrical Distribution Network................................ 3.7 Optimal Taxation................................................................................. 3.8 Location Problems............................................................................... 3.9 Production and Inventory Planning................................................... 3.10 Economic Planning.............................................................................. References........................................................................................................ 88 90 94 103 105 107 114 118 120 4 Optimality Conditions and Duality Theory............................................. 4.1 The Lagrangean Function................................................................... 4.2 Karush-Kuhn-Tucker Optimality Conditions.................................... 4.3 Duality Theoty and Postoptimality Analysis.................................... 4.3.1 The Wolfe Dual Problem........................................................ 4.3.2 The Lagrangean Dual Problem.............................................. 4.3.3 Perturbations, Stability and Computational Aspects...........
References........................................................................................................ 123 124 132 146 147 154 163 171 5 General Solution Methods for Constrained Optimization.................... 5.1 Barrier and Penalty Methods.............................................................. 5.2 Everett’s Lagrangean Multiplier Method.......................................... 5.3 Augmented Lagrangean Methods...................................................... References........................................................................................................ 173 174 186 188 193 6 Methods for Linearly Constrained Problems.......................................... 6.1 Problems with Quadratic Objective................................................... 6.1.1 Wolfe’s Method...................................................................... 6.1.2 The Linear Complementarity Problem................................. 6.2 Problems with Differentiable Convex Objective.............................. 6.2.1 The Method of Frank and Wolfe........................................... 6.2.2 The Gradient Projection Method for Linear Constraints. . 6.3 Problems with Nonconvex Quadratic Objective.............................. References........................................................................................................ 195 195 200 208 216 217 221 232 241 7 Methods for Nonlinearly Constrained Problems.................................... 7.1 Problems with Linear Objective Function......................................... 7.2 Problems with
Convex Objective...................................................... 7.2.1 Problems with Differentiable Objective............................... 7.2.2 Problems with Nondifferentiable Objective......................... 7.3 Problems with Concave Objective..................................................... 7.4 D.C., Conic, and Semidefinite Programming.................................... 7.4.1 D.C. Programming.................................................................. 7.4.2 Conic and Semidefinite Programming.................................. References........................................................................................................ 243 243 249 249 257 264 271 271 273 277
Contents 8 ix Geometric Programming............................................................................. 8.1 Fundamental Concepts of Geometric Programming........................ 8.2 Duality Theory for Geometric Programming.................................... 8.3 Solution Techniques for Geometric Programming Problems.......... 8.3.1 Solution Techniques for Unconstrained Posynomial Geometric Programming Problems....................................... 8.3.2 Solution Techniques for Constrained Posynomial Geometric Programming........................................................ 8.4 Signomial Geometric Programming.................................................. 8.5 Transformations and Illustrations....................................................... References........................................................................................................ 279 279 286 296 296 Appendices............................................................................................................ Appendix A Matrices...................................................................................... Appendix В Systems of Simultaneous Linear Relations............................. Appendix C Convexity and Cones................................................................ Appendix D The Simplex Method for Linear Programming...................... 329 329 332 341 343 References.............................................................................................................. 349
Index....................................................................................................................... 361 307 316 319 328
|
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| author | Eiselt, Horst A. 1950- Sandblom, Carl-Louis |
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| id | DE-604.BV046201682 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:38:05Z |
| institution | BVB |
| isbn | 9783030194611 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031580806 |
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| physical | xii, 366 Seiten Illustrationen |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Springer |
| record_format | marc |
| series | International series in operations research & management science |
| series2 | International series in operations research & management science |
| spelling | Eiselt, Horst A. 1950- Verfasser (DE-588)133413780 aut Nonlinear optimization methods and applications H. A. Eiselt, Carl-Louis Sandblom Cham, Switzerland Springer [2019] © 2019 xii, 366 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science volume 282 Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Sandblom, Carl-Louis Verfasser (DE-588)170403823 aut Erscheint auch als Online-Ausgabe 978-3-030-19462-8 International series in operations research & management science volume 282 (DE-604)BV011630976 282 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031580806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eiselt, Horst A. 1950- Sandblom, Carl-Louis Nonlinear optimization methods and applications International series in operations research & management science Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Nonlinear optimization methods and applications |
| title_auth | Nonlinear optimization methods and applications |
| title_exact_search | Nonlinear optimization methods and applications |
| title_full | Nonlinear optimization methods and applications H. A. Eiselt, Carl-Louis Sandblom |
| title_fullStr | Nonlinear optimization methods and applications H. A. Eiselt, Carl-Louis Sandblom |
| title_full_unstemmed | Nonlinear optimization methods and applications H. A. Eiselt, Carl-Louis Sandblom |
| title_short | Nonlinear optimization |
| title_sort | nonlinear optimization methods and applications |
| title_sub | methods and applications |
| topic | Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031580806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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