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A theorem on the convergence of algorithms of static stochastic optimization

100%

Koronacki J.

Mathematica Applicanda

1976

tom 4

nr 7

The problem of this paper is to minimize a function f, which is scalar-valued and defined on a finite dimensional vector space. An iterative algorithm is of the form X(n+1)=A(n)(X(n)) and can take the usual form X(n+1)=X(n)−a(n)Y(n), where Y(n) can be as in the Kiefer-Wolfowitz procedure, but an is random. Making use of the theorem on convergence of supermartingales the author gives several theorems on the convergence of the procedure to the minimal point of f.

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1 Mathematica Applicanda

1 Koronacki J.

1 1976

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A theorem on the convergence of algorithms of static stochastic optimization