In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient ext...In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.展开更多
Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate i...Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.展开更多
This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorpor...This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorporates inertial techniques and the projection and contraction method.The weak convergence is proved without the condition of the Lipschitz continuity of the mappings.Meanwhile,the linear convergence of the algorithm is established under strong pseudomonotonicity and Lipschitz continuity assumptions.The main results obtained in this paper extend and improve some related works in the literature.展开更多
基金funded by the University of Science,Vietnam National University,Hanoi under project number TN.21.01。
文摘In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.
文摘Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.
文摘This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorporates inertial techniques and the projection and contraction method.The weak convergence is proved without the condition of the Lipschitz continuity of the mappings.Meanwhile,the linear convergence of the algorithm is established under strong pseudomonotonicity and Lipschitz continuity assumptions.The main results obtained in this paper extend and improve some related works in the literature.
