Optimization and Operations Research: Proceedings of a Conference held at Oberwolfach, July 27 - August 2, 1975 (Lecture Notes in Economics and ... in Economics and Mathematical Systems, 117) - Tapa blanda

 
9783540076162: Optimization and Operations Research: Proceedings of a Conference held at Oberwolfach, July 27 - August 2, 1975 (Lecture Notes in Economics and ... in Economics and Mathematical Systems, 117)
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ISBN 10: 3540076166 ISBN 13: 9783540076162
Editorial: Springer, 1976

Sinopsis

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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Reseña del editor

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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Editorial
Springer
Año de publicación
1976
Idioma
Inglés
ISBN 10 
3540076166
ISBN 13 
9783540076162
Encuadernación
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Número de páginas
328
Editor
Oettli W.
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Otras ediciones populares con el mismo título

9780387076164: Optimization and Operations Research. Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975

Edición Destacada

ISBN 10:  0387076166 ISBN 13:  9780387076164
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