Lecture Notes in Economics and Mathematical Systems

Optimization and Operations Research

Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975

Editors: Oettli, W., Ritter, K. (Eds.)

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About this book

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.

Table of contents (27 chapters)

Table of contents (27 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-642-46329-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA in USD
  • ISBN 978-3-540-07616-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Optimization and Operations Research
Book Subtitle
Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975
Editors
  • W. Oettli
  • K. Ritter
Series Title
Lecture Notes in Economics and Mathematical Systems
Series Volume
117
Copyright
1976
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin · Heidelberg
eBook ISBN
978-3-642-46329-7
DOI
10.1007/978-3-642-46329-7
Softcover ISBN
978-3-540-07616-2
Series ISSN
0075-8442
Edition Number
1
Number of Pages
IV, 318
Number of Illustrations
8 b/w illustrations
Topics