Abstract
We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.
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Li, L., Song, W. A modified extragradient method for inverse-monotone operators in Banach spaces. J Glob Optim 44, 609–629 (2009). https://doi.org/10.1007/s10898-008-9361-3
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DOI: https://doi.org/10.1007/s10898-008-9361-3
Keywords
- Extragradient method
- Uniformly convex and uniformly smooth Banach space
- Weakly sequentially continuous
- Inverse-monotone operators
- Weak convergence