In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its cor...In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its corresponding boundary variational inequality and the existence and uniqueness, of solution are given. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.展开更多
The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation...The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.展开更多
We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping...We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.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
The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due...The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.展开更多
By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach spa...By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach space. The results improve and extend the corresponding results shown recentlv.展开更多
This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational in...This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.展开更多
A new descent method for solving mixed variational inequalities is developed based on the auxiliary principle problem. Convergence of the proposed method is also demonstrated.
The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral friction...The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential form.First,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational inequality.Then,we prove the solvability of the contact problem.Finally,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.展开更多
文摘In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its corresponding boundary variational inequality and the existence and uniqueness, of solution are given. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.
基金received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement(823731-CONMECH)supported by the National Science Center of Poland under Maestro Project(UMO-2012/06/A/ST1/00262)+3 种基金National Science Center of Poland under Preludium Project(2017/25/N/ST1/00611)supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland(3792/GGPJ/H2020/2017/0)Qinzhou University Project(2018KYQD06)National Natural Sciences Foundation of Guangxi(2018JJA110006)
文摘The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.
基金supported by the Scientific Research Foundation of Sichuan Normal University(20151602)National Natural Science Foundation of China(10671135,61179033)and the Key Project of Chinese Ministry of Education(212147)
文摘We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.
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This research was supported by MOEC (20060284001)NSFC (70371019 and 10571083)supported partly by NSFC 70571034
文摘The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department (Grant No.07ZA098)a grant from the "project 211(Phase Ⅲ)"the Scientific Research Fund of the Southwestern University of Finance and Economics
文摘By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach space. The results improve and extend the corresponding results shown recentlv.
基金supported by the Natural Science Foundation of China under Grant No.11001287the Natural Science Foundation Project of CSTC under Grant No.2010BB9254
文摘This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.
基金supported by the National Natural Science Foundation of China under Grant No.71201093the Research Fund for Doctoral Program of Ministry of Education of China under Grant No.20120131120084+1 种基金the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province under Grant No.BS2012SF012the Independent Innovation Foundation of Shandong University under Grant No.IFYT14011
文摘A new descent method for solving mixed variational inequalities is developed based on the auxiliary principle problem. Convergence of the proposed method is also demonstrated.
基金The project supported by the NNSF of China Grants Nos.12001478,12026255,12026256 and 11961074,H2020-MSCA-RISE-2018 ResearchInnovation Staff Exchange Scheme Fellowship within the Project No.823731 CONMECH+3 种基金National Science Center of Poland under Preludium Project No.2017/25/N/ST1/00611It is also supported by the Startup Project of Doctor Scientific Research of Yulin Normal University No.G2020ZK07Natural Science Foundation of Guangxi Province Grants Nos.2018GXNSFDA281028 and 2020GXNSFBA297137the High Level Innovation Team Program from Guangxi Higher Education Institutions of China(Document no.[2018]35).
文摘The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential form.First,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational inequality.Then,we prove the solvability of the contact problem.Finally,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.
