Optimization and Operations Research: Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975
The variable metric algorithm is widely recognised as one of the most efficient ways of solving the following problem:- Locate x* a local minimum point n ( 1) of f(x) x E R Considerable attention has been given to the study of the convergence prop- ties of this algorithm especially for the case wher...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1976
|
| Ausgabe: | 1st ed. 1976 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
117 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | The variable metric algorithm is widely recognised as one of the most efficient ways of solving the following problem:- Locate x* a local minimum point n ( 1) of f(x) x E R Considerable attention has been given to the study of the convergence prop- ties of this algorithm especially for the case where analytic expressions are avai- ble for the derivatives g. = af/ax. i 1 ••• n • (2) ~ ~ In particular we shall mention the results of Wolfe (1969) and Powell (1972), (1975). Wolfe established general conditions under which a descent algorithm will converge to a stationary point and Powell showed that two particular very efficient algorithms that cannot be shown to satisfy \,olfe's conditions do in fact converge to the minimum of convex functions under certain conditions. These results will be st- ed more completely in Section 2. In most practical problems analytic expressions for the gradient vector g (Equ. 2) are not available and numerical derivatives are subject to truncation error. In Section 3 we shall consider the effects of these errors on Wolfe's convergent prop- ties and will discuss possible modifications of the algorithms to make them reliable in these circumstances. The effects of rounding error are considered in Section 4, whilst in Section 5 these thoughts are extended to include the case of on-line fu- tion minimisation where each function evaluation is subject to random noise |
| Beschreibung: | 1 Online-Ressource (IV, 318 p. 8 illus) |
| ISBN: | 9783642463297 |
| DOI: | 10.1007/978-3-642-46329-7 |
Internformat
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| 245 | 1 | 0 | |a Optimization and Operations Research |b Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 |c herausgegeben von W. Oettli, K. Ritter |
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| 490 | 0 | |a Lecture Notes in Economics and Mathematical Systems |v 117 | |
| 520 | |a The variable metric algorithm is widely recognised as one of the most efficient ways of solving the following problem:- Locate x* a local minimum point n ( 1) of f(x) x E R Considerable attention has been given to the study of the convergence prop- ties of this algorithm especially for the case where analytic expressions are avai- ble for the derivatives g. = af/ax. i 1 ••• n • (2) ~ ~ In particular we shall mention the results of Wolfe (1969) and Powell (1972), (1975). Wolfe established general conditions under which a descent algorithm will converge to a stationary point and Powell showed that two particular very efficient algorithms that cannot be shown to satisfy \,olfe's conditions do in fact converge to the minimum of convex functions under certain conditions. These results will be st- ed more completely in Section 2. In most practical problems analytic expressions for the gradient vector g (Equ. 2) are not available and numerical derivatives are subject to truncation error. In Section 3 we shall consider the effects of these errors on Wolfe's convergent prop- ties and will discuss possible modifications of the algorithms to make them reliable in these circumstances. The effects of rounding error are considered in Section 4, whilst in Section 5 these thoughts are extended to include the case of on-line fu- tion minimisation where each function evaluation is subject to random noise | ||
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-3-642-46329-7 |
| edition | 1st ed. 1976 |
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| spelling | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 herausgegeben von W. Oettli, K. Ritter 1st ed. 1976 Berlin, Heidelberg Springer Berlin Heidelberg 1976 1 Online-Ressource (IV, 318 p. 8 illus) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 117 The variable metric algorithm is widely recognised as one of the most efficient ways of solving the following problem:- Locate x* a local minimum point n ( 1) of f(x) x E R Considerable attention has been given to the study of the convergence prop- ties of this algorithm especially for the case where analytic expressions are avai- ble for the derivatives g. = af/ax. i 1 ••• n • (2) ~ ~ In particular we shall mention the results of Wolfe (1969) and Powell (1972), (1975). Wolfe established general conditions under which a descent algorithm will converge to a stationary point and Powell showed that two particular very efficient algorithms that cannot be shown to satisfy \,olfe's conditions do in fact converge to the minimum of convex functions under certain conditions. These results will be st- ed more completely in Section 2. In most practical problems analytic expressions for the gradient vector g (Equ. 2) are not available and numerical derivatives are subject to truncation error. In Section 3 we shall consider the effects of these errors on Wolfe's convergent prop- ties and will discuss possible modifications of the algorithms to make them reliable in these circumstances. The effects of rounding error are considered in Section 4, whilst in Section 5 these thoughts are extended to include the case of on-line fu- tion minimisation where each function evaluation is subject to random noise Operations Research/Decision Theory Operations research Decision making Optimierung (DE-588)4043664-0 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1975 Oberwolfach gnd-content Operations Research (DE-588)4043586-6 s Optimierung (DE-588)4043664-0 s DE-604 Oettli, W. edt Ritter, K. edt Erscheint auch als Druck-Ausgabe 9783540076162 Erscheint auch als Druck-Ausgabe 9783642463303 https://doi.org/10.1007/978-3-642-46329-7 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 Operations Research/Decision Theory Operations research Decision making Optimierung (DE-588)4043664-0 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4043586-6 (DE-588)1071861417 |
| title | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 |
| title_auth | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 |
| title_exact_search | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 |
| title_exact_search_txtP | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 |
| title_full | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 herausgegeben von W. Oettli, K. Ritter |
| title_fullStr | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 herausgegeben von W. Oettli, K. Ritter |
| title_full_unstemmed | Optimization and Operations Research Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 herausgegeben von W. Oettli, K. Ritter |
| title_short | Optimization and Operations Research |
| title_sort | optimization and operations research proceedings of a conference held at oberwolfach july 27 august 2 1975 |
| title_sub | Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975 |
| topic | Operations Research/Decision Theory Operations research Decision making Optimierung (DE-588)4043664-0 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Operations Research/Decision Theory Operations research Decision making Optimierung Operations Research Konferenzschrift 1975 Oberwolfach |
| url | https://doi.org/10.1007/978-3-642-46329-7 |
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