An Algorithm for Solving Triple Hierarchical Pseudomonotone Variational Inequalities
نویسندگان
چکیده
In this paper, we introduce and analyze a hybrid steepest-descent extragradient algorithm for solving triple hierarchical pseudomonotone variational inequalities in a real Hilbert space. The proposed algorithm is based on Korpelevich’s extragradient method, Mann’s iteration method, hybrid steepest-descent method and Halpern’s iteration method. Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is derived. Our results improve and extend the corresponding results in the earlier and recent literature.
منابع مشابه
An analytic center cutting plane method for pseudomonotone variational inequalities
We consider an analytic center algorithm for solving generalized monotone variational inequalities in R", which adapts a recent result due to Goffin et al. (1993) to the numerical resolution of continuous pseudomonotone variational inequalities.
متن کاملψ-pseudomonotone generalized strong vector variational inequalities with application
In this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in Hilbert spaces.
متن کاملOn the Vector Variational-like Inequalities with Relaxed η-α Pseudomonotone Mappings
In this paper we introduce some new conditions of the solu- tions existence for variational-like inequalities with relaxed &eta-&alpha pseu- domonotone mappings in Banach spaces. The advantage of these new conditions is that they are easier to be veried than those that appear in some of the previous corresponding articles.
متن کاملAn Inexact Proximal Algorithm for Pseudomonotone and Quasimonotone Variational Inequalities
In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generates by the algorithm is convergent for the pseudomonotone case and weakly convergent for the quasimonotone ones. This approach unifies the results o...
متن کاملCommon solutions to pseudomonotone equilibrium problems
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from the previously known one for variational inequalities to equilibrium problems. The second is a new cyclic hybrid extragradient-cutting algorithm....
متن کامل