Optimization and Operations Research

K. Ritter

ISBN 10: 3540076166 / ISBN 13: 9783540076162

Edité par Springer Berlin Heidelberg, Springer Berlin Heidelberg Feb 1976, 1976

A propos de cet article

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 328 pp. Englisch.

N° de réf. du vendeur 9783540076162

Détails bibliographiques

• Titre: Optimization and Operations Research
• Éditeur: Springer Berlin Heidelberg, Springer Berlin Heidelberg Feb 1976
• Date de parution: 1976
• Langue: anglais
• ISBN à 10 chiffres: 3540076166
• ISBN à 13 chiffres: 9783540076162
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 244 L x 170 H x 18 P (en millimètres) 244 millimètres de largeur par 170 millimètres de hauteur par 18 millimètres de profondeur
• Poids: 568 grammes

A propos de ce titre

Synopsis

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.