It is known that stepsize’s choice plays a key role in convergence and efficiency of the extragradient method, which is a special projection-type method, for solving monotone variational inequality problems. In this ...It is known that stepsize’s choice plays a key role in convergence and efficiency of the extragradient method, which is a special projection-type method, for solving monotone variational inequality problems. In this paper, by analyzing the existing stepsize rules, a predictor stepsize rule without the bounded restriction is proposed, and a corrector stepsize rule with (approximate) optimality is also presented. The corresponding convergence properties and numerical examples are shown.展开更多
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
In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. More...In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. Moreover, weak convergence and R-linear convergence analyses of the algorithm are constructed under appropriate assumptions. Finally, the efficiency of the proposed algorithm is demonstrated through numerical implementations.展开更多
In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our me...In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.展开更多
This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combi...This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.展开更多
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of ...The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.展开更多
Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving q...Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.展开更多
In this paper,we investigate a new inertial viscosity extragradient algorithm for solving variational inequality problems for pseudo-monotone and Lipschitz continuous operator and fixed point problems for quasi-nonexp...In this paper,we investigate a new inertial viscosity extragradient algorithm for solving variational inequality problems for pseudo-monotone and Lipschitz continuous operator and fixed point problems for quasi-nonexpansive mappings in real Hilbert spaces.Strong convergence theorems are obtained under some appropriate conditions on the parameters.Finally,we give some numerical experiments to show the advantages of our proposed algorithms.The results obtained in this paper extend and improve some recent works in the literature.展开更多
Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method a...Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator’s partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms.展开更多
许多算法被提出用来解决变分不等式问题,其中最简单的是G.M.Korpelevich(Matecon,1976,12:747-756.)超梯度算法.此算法被许多学者所改进.其中文献(Y.J.Wang,N.H.Xiu,J.Z.Zhang.JOptim Theory Appl,2003,119:167-168.)改进的超梯度算法...许多算法被提出用来解决变分不等式问题,其中最简单的是G.M.Korpelevich(Matecon,1976,12:747-756.)超梯度算法.此算法被许多学者所改进.其中文献(Y.J.Wang,N.H.Xiu,J.Z.Zhang.JOptim Theory Appl,2003,119:167-168.)改进的超梯度算法不用假设解存在,并且可以通过迭代产生的点列的收敛性检验解的存在性.将Y.J.Wang,N.H.Xiu和J.Z.Zhang改进的超梯度算法推广到无穷维Hilbert空间,并讨论在无穷维Hilbert空间中改进的超梯度算法的迭代序列关于伪单调变分不等式的解的强收敛性质.展开更多
文摘It is known that stepsize’s choice plays a key role in convergence and efficiency of the extragradient method, which is a special projection-type method, for solving monotone variational inequality problems. In this paper, by analyzing the existing stepsize rules, a predictor stepsize rule without the bounded restriction is proposed, and a corrector stepsize rule with (approximate) optimality is also presented. The corresponding convergence properties and numerical examples are shown.
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In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. Moreover, weak convergence and R-linear convergence analyses of the algorithm are constructed under appropriate assumptions. Finally, the efficiency of the proposed algorithm is demonstrated through numerical implementations.
基金funded by National University ofCivil Engineering(NUCE)under grant number 15-2020/KHXD-TD。
文摘In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.
文摘This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.
基金Supported by King Mongkut's University of Technology Thonburi.KMUTT,(CSEC Project No.E01008)supported by the Faculty of Applied Liberal Arts RMUTR Research Fund and King Mongkut's Diamond scholarship for fostering special academic skills by KMUTT
文摘The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.
基金Supported by NSFC (Nos.11771063,12171062)Natural Science Foundation of Chongqing(No.cstc2020jcyj-msxmX0455)Science and Technology Project of Chongqing Education Committee (No.KJZD-K201900504)。
文摘Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.
基金Supported by the NSF of China(Grant Nos.11771063,11971082 and 12171062)the Natural Science Foundation of Chongqing(Grant No.cstc2020jcyj-msxm X0455)+2 种基金Science and Technology Project of Chongqing Education Committee(Grant No.KJZD-K201900504)the Program of Chongqing Innovation Research Group Project in University(Grant No.CXQT19018)Open Fund of Tianjin Key Lab for Advanced Signal Processing(Grant No.2019ASP-TJ03)。
文摘In this paper,we investigate a new inertial viscosity extragradient algorithm for solving variational inequality problems for pseudo-monotone and Lipschitz continuous operator and fixed point problems for quasi-nonexpansive mappings in real Hilbert spaces.Strong convergence theorems are obtained under some appropriate conditions on the parameters.Finally,we give some numerical experiments to show the advantages of our proposed algorithms.The results obtained in this paper extend and improve some recent works in the literature.
文摘Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator’s partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms.
文摘许多算法被提出用来解决变分不等式问题,其中最简单的是G.M.Korpelevich(Matecon,1976,12:747-756.)超梯度算法.此算法被许多学者所改进.其中文献(Y.J.Wang,N.H.Xiu,J.Z.Zhang.JOptim Theory Appl,2003,119:167-168.)改进的超梯度算法不用假设解存在,并且可以通过迭代产生的点列的收敛性检验解的存在性.将Y.J.Wang,N.H.Xiu和J.Z.Zhang改进的超梯度算法推广到无穷维Hilbert空间,并讨论在无穷维Hilbert空间中改进的超梯度算法的迭代序列关于伪单调变分不等式的解的强收敛性质.
