A new hybrid iterative algorithm for variational inequalities

doi:10.1016/j.amc.2010.01.087

A new hybrid iterative algorithm for variational inequalities

2010-04-01

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DOI：10.1016/j.amc.2010.01.087

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Let H be a real Hilbert space. Let F:H -> H be a strongly monotone and Lipschitzian mapping. Let {T(n)}(n-1)(infinity):H -> H be an infinite family of non-expansive mappings with common fixed point set boolean AND(infinity)(n-1) Fix(T(n))not equal empty set. We devise an iterative algorithm {y(n) = x(n) - lambda(n)F(x(n)), x(n+1) = (1-alpha(n))y(n) + alpha(n)W(n)y(n), n >= 0, where {lambda(n)} is asequence in (0, infinity), {alpha(n)} is a sequence in (0,1) and W(n) is the W-mapping. We prove that the sequence {x(n)} converges in norm to x* is an element of boolean AND(infinity)(n-1) Fix(T(n)) which is the unique solution of the following variational inequality < Fx*, x-x*> >= 0, for all x is an element of boolean AND(infinity)(n=1)Fix(T(n)), (C) 2010 Elsevier Inc. All rights reserved.

Keywords:

Hybrid algorithm

Non-expansive mapping

Variational inequality

Hilbert spaces

A new hybrid iterative algorithm for variational inequalities

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