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We are focused on solving a general class of bilevel variational inequalities involving quasimonotone operators in real Hilbert spaces. A strong convergent iterative method for solving the problem is presented and analysed. Our work generalizes several existing results in the literature and holds two major mathematical advantages. 1) Any generated sequence by the algorithm preserves the Fejér monotonicity property; and 2) There is no need to execute a line-search or know a-prior the strongly monotone coefficient or Lipschitz constant. Numerical experiments with comparisons to existing/related methods illustrate the performances of the proposed method and in particular, application to optimal control problems suggests the practical potential of our scheme. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature. [ABSTRACT FROM AUTHOR]

Abstract In this article, we introduce an inertial-type algorithm that combines the extragradient subgradient method, the projection contraction method, and the viscosity method. The proposed method is used for solving quasimonotone variational inequality problems in infinite dimensional real Hilbert spaces such that it does not depend on the Lipschitz constant of the cost operator. Further, we prove the strong convergence results of the new algorithm. Our strong convergence results are achieved without imposing strict conditions on the control parameters and inertial factor of our algorithm. We utilize our algorithm to solve some problems in applied sciences and engineering such as image restoration and optimal control. Some numerical experiments are carried out to support our theoretical results. Our numerical illustrations show that our new method is more efficient than many existing methods.

In this article, we introduce an inertial-type algorithm that combines the extragradient subgradient method, the projection contraction method, and the viscosity method. The proposed method is used for solving quasimonotone variational inequality problems in infinite dimensional real Hilbert spaces such that it does not depend on the Lipschitz constant of the cost operator. Further, we prove the strong convergence results of the new algorithm. Our strong convergence results are achieved without imposing strict conditions on the control parameters and inertial factor of our algorithm. We utilize our algorithm to solve some problems in applied sciences and engineering such as image restoration and optimal control. Some numerical experiments are carried out to support our theoretical results. Our numerical illustrations show that our new method is more efficient than many existing methods. [ABSTRACT FROM AUTHOR]