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| Content Provider | Springer Nature Link |
|---|---|
| Author | Neumaier, A. Elster, C. |
| Copyright Year | 1997 |
| Abstract | The optimization of noisy functions in a few variables only is a common problem occurring in various applications, for instance in finding the optimal choice of a few control parameters in chemical experiments. The traditional tool for the treatment of such problems is the method of Nelder-Mead (NM). In this paper an alternative method based on a trust region approach (TR) is offered and compared to Nelder-Mead. On the standard collection of test functions for unconstrained optimization by Moré et al. [9], TR performs substantially more robust than NM. If performance is measured by the number of function evaluations, TR is on the average twice as fast as NM.Die Optimierung verrauschter Funktionen in einer geringen Zahl von Variablen ist ein häufig in Anwendungen vorkommendes Problem, z.B. um die optimale Wahl einiger Kontrollparameter in chemischen Experimenten zu finden. Das traditionelle Werkzeug zur Behandlung solcher Probleme ist das Verfahren von Nelder-Mead (NM). In dieser Arbeit wird eine auf Vertrauensbereichen beruhende Alternative (TR) vorgestellt und mit Nelder-Mead verglichen. Auf Moré et al.’s bekannter Sammlung von Testfunktionen für Optimierung ohne Nebenbedingungen arbeitet TR wesentlich robuster als NM. Mißt man die Qualität an der Zahl der Funktionsauswertungen, so ist TR im Mittel doppelt so schnell wie NM. |
| Ending Page | 46 |
| Page Count | 16 |
| Starting Page | 31 |
| File Format | |
| ISSN | 0010485X |
| e-ISSN | 14365057 |
| Journal | Computing |
| Issue Number | 1 |
| Volume Number | 58 |
| Language | German |
| Publisher | Springer-Verlag |
| Publisher Date | 1997-01-01 |
| Publisher Place | Vienna |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Computational Mathematics and Numerical Analysis Unconstrained optimization trust region method quadratic model noisy functions Nelder-Mead method Nonlinear programming |
| Content Type | Text |
| Resource Type | Article |
| Subject | Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics Numerical Analysis Computer Science Applications Software |
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