A theorem on the convergence of algorithms of static stochastic optimization

J. Koronacki. "A theorem on the convergence of algorithms of static stochastic optimization." Mathematica Applicanda 4.7 (1976): null. <http://eudml.org/doc/293293>.

@article{J1976,
abstract = {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.},
author = {J. Koronacki},
journal = {Mathematica Applicanda},
keywords = {93E10},
language = {eng},
number = {7},
pages = {null},
title = {A theorem on the convergence of algorithms of static stochastic optimization},
url = {http://eudml.org/doc/293293},
volume = {4},
year = {1976},
}

TY - JOUR
AU - J. Koronacki
TI - A theorem on the convergence of algorithms of static stochastic optimization
JO - Mathematica Applicanda
PY - 1976
VL - 4
IS - 7
SP - null
AB - 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.
LA - eng
KW - 93E10
UR - http://eudml.org/doc/293293
ER -