Optimization of Functions whose Values are Subject to Small Errors
1977 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 17, no 2, 160-169 p.Article in journal (Refereed) Published
In this paper we consider the minimization of a function whose values can only be obtained with an error. For the case when the error has certain statistical properties this problem has been investigated by Kiefer and Wolfowitz (1) and Kushner (2, 3). Kushner has shown that a certain class of algorithms converge to a stationary point with probability one. Here a different approach is used. The error is assumed to have an upper bound and it is shown that a stationary point can be obtained to within a certain accuracy, dependent on the magnitude of the error. Our results are related to works concerning roundoff errors for one dimensional optimization (4) and solution of nonlinear equations (5). The algorithm we use can be regarded as an extension of the methods used in (6), (8) and (9).
Place, publisher, year, edition, pages
Kluwer Academic Publishers, 1977. Vol. 17, no 2, 160-169 p.
Minimization, Nonlinear equations
IdentifiersURN: urn:nbn:se:liu:diva-100860DOI: 10.1007/BF01932287OAI: oai:DiVA.org:liu-100860DiVA: diva2:664057