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Convergence w.p.1 for Unconstrained Systems

  • Harold J. Kushner
  • Dean S. Clark
Part of the Applied Mathematical Sciences book series (AMS, volume 26)

Abstract

In this chapter, we will use some simple compactness ideas in order to prove w.p.1 convergence for a variety of unconstrained SA methods. The asymptotic properties of the SA {Xn| sequence will be shown to be the same as the asymptotic properties of the solution to an ordinary differential equation, or generalized ordinary differential equation. We will not aim at the most comprehensive results, but will try to develop the general ideas. The basic idea is simply an extension of the compactness technique as used to construct solutions to ordinary differential equations (Coddington and Levinson [C2], pp. 42–45).

Keywords

Asymptotic Property Noise Condition Convergent Subsequence Uniform Continuity Piecewise Linear Interpolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1978

Authors and Affiliations

  • Harold J. Kushner
    • 1
  • Dean S. Clark
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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