%A M. V. Solodov
%A S. K. Zavriev
%T Stability Properties of the Gradient Projection Method
%T with Applications to the Backpropagation Algorithm
%D June 1994
%R 94-05
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X Convergence properties of the generalized
are investigated. It is shown that every trajectory of the method is
attracted, in a certain sense, to an $\varepsilon$-stationary set
of the problem,
where $\varepsilon$ depends on the magnitude of the perturbations.
Estimates for the attraction sets of the iterates
are given in the general (nonsmooth and nonconvex) case.
In the convex case, our results imply
convergence to an $\epsilon$-optimal set. The results are
further strengthened for weakly sharp and strongly convex problems.
Convergence of the parallel algorithm in the case of the additive
objective function is established.
One of the principal applications of our results is the stability analysis of
the classical backpropagation algorithm for training
artificial neural networks.