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Applicational aspects of stochastic approximation

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Stochastic Approximation and Optimization of Random Systems

Part of the book series: DMV Seminar ((OWS,volume 17))

Abstract

Let F(x) be a real function defined on ℝk or a subset of it. In this part we will consider the optimization problem \((P)\parallel \begin{array}{*{20}c} {F(x) = \min !} \\ {x \in S} \\ \end{array}\)where S \(\subseteq \) ℝk is a set of constraints. Any point x* which is the solution of (P) is called a global minimizer of F on S. If there is an open set U such that a point x 0 is the solution of \((P)\parallel \begin{array}{*{20}c} {F(x) = \min !} \\ {x \in S \cap U} \\ \end{array}\) then x 0 is called a local minimizer of F on S. In general, for deterministic procedures which use the gradient f(x) of F(x), only convergence to the set of critical points x: f(x) = 0} can be proved. There are however tricky deterministic methods which avoid convergence to non-global minimizers (Dixon and Szegö 1975; Ge 1990).

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Authors and Affiliations

  1. Institute of Statistics and Computer Science, University of Vienna, Universitätsstrasse 5, A-1010, Wien, Austria

    Georg Pflug

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  1. Georg Pflug
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© 1992 Springer Basel AG

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Pflug, G. (1992). Applicational aspects of stochastic approximation. In: Stochastic Approximation and Optimization of Random Systems. DMV Seminar, vol 17. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8609-3_2

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  • DOI: https://doi.org/10.1007/978-3-0348-8609-3_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-2733-0

  • Online ISBN: 978-3-0348-8609-3

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