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A Stochastic Iteration Method for A Class of Monotone Variational Inequalities In Hilbert Space
Pages - 1 - 6     |    Revised - 30-06-2020     |    Published - 01-08-2020
Volume - 8   Issue - 1    |    Publication Date - August 2020  Table of Contents
Linear Monotone Operator, Hilbert Space, Stochastic Approximation.
We examined a general method for obtaining a solution to a class of monotone variational inequalities in Hilbert space. Let H be a real Hilbert space, and Let T : H -> H be a continuous linear monotone operator and K be a non empty closed convex subset of H. From an initial arbitrary point x0 ∈ K. We proposed and obtained iterative method that converges in norm to a solution of the class of monotone variational inequalities. A stochastic scheme {xn} is defined as follows: x(n+1) = xn - anF* (xn), n≥0, F*(xn), n ≥ 0 is a strong stochastic approximation of Txn - b, for all b (possible zero) ∈ H and an ∈ (0,1).
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