A new hybrid iterative algorithm for variational inequalities

作者：Yao, Yonghong^*; Noor, Muhammad A.; Liou, Yeong-Cheng

来源：Applied Mathematics and Computation, 2010, 216(3): 822-829.

DOI：10.1016/j.amc.2010.01.087

• Hybrid algorithm
• Non-expansive mapping
• Variational inequality
• Hilbert spaces

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 u

• 出版日期2010-4-1
• 单位天津工业大学