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
This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to ...This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.展开更多
In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techn...In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.展开更多
A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general g...A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.展开更多
In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem wit...In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.展开更多
A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven tha...A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.展开更多
An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is est...An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.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
Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to e...Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to enhance the speed of the convergence and reduce computational cost,the algorithms used a new step size and a cutting hyperplane.The first algorithm was proved to be weak convergence,while the second algorithm used a modified version of Halpern iteration to obtain strong convergence.Finally,numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.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
In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the mode...In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.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.
基金Supported by Natural Science Foundation of Shanghai(14ZR1429200)National Science Foundation of China(11171221)+4 种基金Shanghai Leading Academic Discipline Project(XTKX2012)Innovation Program of Shanghai Municipal Education Commission(14YZ094)Doctoral Program Foundation of Institutions of Higher Educationof China(20123120110004)Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)Young Teacher Training Projection Program of Shanghai for Science and Technology
文摘This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.
基金Supported by the NNSF of china(11171221)SuppoSed by the Shanghai Municipal Committee of Science and Technology(10550500800)
文摘In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.
文摘A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.
基金supported by NSF Grant of China(11131005,11301400)Hubei Key Laboratory of Applied Mathematics(Hubei University)
文摘In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.
基金supported by the Key Program of National Natural Science Foundation of China(No.70831005)the National Natural Science Foundation of China(No.10671135)the Fundamental Research Funds for the Central Universities(No.2009SCU11096)
文摘A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.
基金supported by the National Natural Science Foundation of China (10671126)Shanghai Leading Academic Discipline Project(S30501)
文摘An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.
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.
文摘Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to enhance the speed of the convergence and reduce computational cost,the algorithms used a new step size and a cutting hyperplane.The first algorithm was proved to be weak convergence,while the second algorithm used a modified version of Halpern iteration to obtain strong convergence.Finally,numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.
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.
基金the NSF of Guangxi(2021GXNSFFA196004,GKAD23026237)the NNSF of China(12001478)+4 种基金the China Postdoctoral Science Foundation(2022M721560)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECHthe National Science Center of Poland under Preludium Project(2017/25/N/ST1/00611)the Startup Project of Doctor Scientific Research of Yulin Normal University(G2020ZK07)the Ministry of Science and Higher Education of Republic of Poland(4004/GGPJII/H2020/2018/0,440328/Pn H2/2019)。
文摘In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.
