对广义强非线性拟变分包含带有误差的近似点算法

丁协平

对广义强非线性拟变分包含带有误差的近似点算法

丁协平

四川师范大学数学系

基金项目: 四川省教委自然科学基金

详细信息

中图分类号: O177;O176
计量
- 文章访问数: 2363
- HTML全文浏览量: 112
- PDF下载量: 668
- 被引次数: 0
出版历程
- 收稿日期: 1997-02-24
- 刊出日期: 1998-07-15

Proximal Point Algorithm with Errors for Generalized Strongly Nonlinear Quasivariational Inclusions

Ding Xieping

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China

摘要

摘要: 本文研究了一类广义强非线性拟变分包含.在Hilbert空间内利用与极大单调映象相联系的预解算子的性质,对广义强非线性拟变分包含建立了解的存在性定理和建议了一个新的寻求近似解的带有误差的近似总算法,证明了近似解序列强收敛于精确解.作为特例,在此领域内的某些已知结果也被讨论.
- 广义强非线性拟变分包含 /
- 带有误差的近似点算法
Abstract: In this paper,a class of generalized strongly nonlinear quasivariational in clusions are studied.By using the properties of the resolvent opera for associated with amaximal monotone mapping in Hilbert space,an existence theorem of solutions forgene ralized strongly nonlinear quasi variational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly nonlinearquasivariational inclusion.As special cases,some known results in this field are also discussed.
- generalized strongly nonlinear quasivariational inclusion /
- proximal point algorithm with errors

HTML全文

参考文献(14)

[1]	X.P.Ding,Perturbed proximal point algorithm for generalized quasivariationalinclusions,J.Math.Anal.Appl.,210,1(1997),88-101.
[2]	A.Hassouni and A.Moudafi,A perturbed algorithm for variational inclusions,J.Math.Anal.Appl.,185,3(1994),706-721.
[3]	D.Chan and J.S.Pang,The generalized quasivariational inequalitics,Math.Oper.Res.,7,2(1982),211-222.
[4]	X.P.Ding,Generalized strongly nonlinear quasivariational inequalities.J.Math.Anal.Appl.,173,2(1993),577-587.
[5]	X.P.Ding,A new class of generalized strongly nonlinear qusasivariational inequalitiesand quasicomplementarity problems,Indian J.Pure Appl.Math.,25,10(1994),1115-1128.
[6]	X.P.Ding and E.Tarafdar,Monotone generalized variational inequalities andgeneralized complementarity problems,J.Optim.Theory Appl.,88,1(1996),107-122.
[7]	S.C.Fang and E.L.Peterson,Generalized variational inequalities,J.Optim.Theory Appl.,38.2(1982),363-383.
[8]	P.T.Harker and J.S.Pang,Finite-dimensional variational inequality and nonlinearcomplementarity problems:A survey of theory,algorithm and applications,Math.Program,48(1990),161-220.
[9]	M.A.Noor,An iterative scheme for a class of quasivariational inequalities,J.Math.Anal.Appl.,110(1985),462-468.
[10]	M.A.Noor,Generalized multivalued quasivariational inequalities,Computers Math.Appl.,31,12(1996),1-13.
[11]	M.A.Noor,K.I.Noor and T.M.Rassias,Some aspects of variational inequalities,J.Comput.Appl.Math.,47,2(1993),285-312.
[12]	D.Pascali and S.Sburlan,Nonlinear Mappings of Monotone Type,Sijthoff andNoordhoff inter.Pub.Romania(1978).
[13]	R.Saigal,Extension of the generalized complementarity problem,Math.Oper.Res.,1,2(1976),260-266.
[14]	L.Zeng,Iterative algorithm for finding approximate solutions to completely generalizedstrongly nonlinear quasivariational inequalities,J.Math.Anal.Appl.,201,1(1996),180-194.