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Optimization and Operations Research - Proceedings of a Conference Held at Oberwolfach, July 27-August 2, 1975 (English, German, Paperback, Softcover reprint of the original 1st ed. 1976)
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Optimization and Operations Research - Proceedings of a Conference Held at Oberwolfach, July 27-August 2, 1975 (English, German, Paperback, Softcover reprint of the original 1st ed. 1976)
Series: Lecture Notes in Economics and Mathematical Systems, 117
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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.
General
Imprint: |
Springer-Verlag
|
Country of origin: |
Germany |
Series: |
Lecture Notes in Economics and Mathematical Systems, 117 |
Release date: |
February 1976 |
First published: |
1976 |
Editors: |
W. Oettli
• K Ritter
|
Dimensions: |
244 x 170 x 18mm (L x W x T) |
Format: |
Paperback
|
Pages: |
318 |
Edition: |
Softcover reprint of the original 1st ed. 1976 |
ISBN-13: |
978-3-540-07616-2 |
Languages: |
English
•
German
|
Categories: |
Books >
Business & Economics >
General
|
LSN: |
3-540-07616-6 |
Barcode: |
9783540076162 |
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