Abstract
Abstract Korpelevich’s extragradient method has been studied and extended extensively due to its applicability to the whole class of monotone variational inequalities. In the present paper, we propose a variant extragradient-type method for solving monotone variational inequalities. Convergence analysis of the method is presented under reasonable assumptions on the problem data. MSC:47H05, 47J05, 47J25.
Highlights
Let H be a real Hilbert space with the inner product ·, · and its induced norm ·
The variational inequality problem is a fundamental problem in variational analysis and, in particular, in optimization theory
Motivated by the works given above, in the present paper, we propose a variant extragradient-type method for solving monotone variational inequalities
Summary
Let H be a real Hilbert space with the inner product ·, · and its induced norm ·. See [ ] for convergence properties of this method for the case in which f is convex and f : Rn → R is a differentiable function, which are related to the results in this article. Convergence results for this method require some monotonicity properties of A. It is known that Korpelevich’s method ( ) has only weak convergence in the infinite-dimensional Hilbert spaces (please refer to a recent result of Censor et al [ ] and [ ]).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
