平衡问题变分包含问题及不动点问题的二次极小化

张石生; 李向荣; 陈志坚

doi:10.3879/j.issn.1000-0887.2010.07.013

平衡问题变分包含问题及不动点问题的二次极小化

doi: 10.3879/j.issn.1000-0887.2010.07.013

宜宾学院数学系,四川宜宾 644007;2.香港理工大学应用数学系,香港九龙

基金项目: 宜宾学院自然科学基金(2009-Z003)的资助

详细信息

作者简介:
张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);李向荣(E-mail:majlee@polyu.edu.hk);陈志坚(E-mail:machanck@polyu.edu.hk).

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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-05-30
- 刊出日期: 2010-07-15

Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem

Department of Mathematics, Yibin University, Yibin, Sichuan 644007, P. R. China;

摘要

摘要: 借助预解式技巧,寻求二次极小化问题minx∈Ω‖x‖2的解,其中Ω是Hilbert空间中某一广义平衡问题的解集,与一无穷族非扩张映像的公共不动点的集合，以及某一变分包含的解集的交集．在适当的条件下，逼近上述极小化问题的解的一新的强收敛定理被证明．
- 二次极小化问题 /
- 广义平衡问题 /
- 变分包含 /
- 多值极大单调映像 /
- 逆强单调映像 /
- 预解算子 /
- 不动点 /
- 非扩张映像
Abstract: The purpose was by using the resolvent approach to find the solutions to the quad-raticminimization problem: min_x∈Ω||x||², where Ω was the intersection set of the set of solutions to some generalized equilibrium problem, the set of common fixed points for an infinite family of nonexpansive mappings and the set of solutions to some variational in clusions in the setting of Hilbert spaces. Under suitable conditions some new strong convergence theorems for approximating to a solution of the above minimization problem were proved.
- quadratic minimization problem /
- generalized equilibrium problem /
- variational inclusion /
- multi-valued maximal monotone mapping /
- inverse-strongly monotone mapping /
- resolvent operator /
- fixed point /
- nonexpansive mapping

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参考文献(15)

[1]	Noor M A, Noor K I. Sensitivity analysis of quasi variational inclusions[J].J Math Anal Appl, 1999, 236(2):290-299. doi: 10.1006/jmaa.1999.6424
[2]	Chang S S. Set-valued variational inclusions in Banach spaces[J].J Math Anal Appl, 2000, 248(2): 438-454. doi: 10.1006/jmaa.2000.6919
[3]	Chang S S. Existence and approximation of solutions of set-valued variational inclusions in Banach spaces[J]. Nonlinear Anal, 2001, 47(1): 583-594. doi: 10.1016/S0362-546X(01)00203-6
[4]	Demyanov V F, Stavroulakis G E, Polyakova L N, Panagiotopoulos P D.Quasidifferentiability and Nonsmooth Modeling in Mechanics, Engineering and Economics[M].Dordrecht: Kluwer Academic, 1996.
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[8]	Iiduka H, Takahashi W, Toyoda M. Approximation of solutions of variational inequalities for monotone mappings[J]. Pan-Amer Math J, 2004, 14: 49-61.
[9]	张石生，李向荣，陈志坚.拟变分包含及不动点问题公解的算法[J].应用数学和力学，2008， 29(5): 515-524.
[10]	Blum E, Oettli W. From optimization and variational inequalities problems[J].Math Stud, 1994, 63: 123-145.
[11]	Bruck R E. Properties of fixed point sets of nonexpansive mappings in Banach spaces[J]. Trans Amer Math Soc, 1973, 179: 251-262. doi: 10.1090/S0002-9947-1973-0324491-8
[12]	Suzuki T. Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces[J]. Fixed Point Theory Appl, 2005, 2005(1): 103-123.
[13]	Pascali Dan. Nonlinear Mappings of Monotone Type[M].The Netherlands: Sijthoff and Noordhoff International Publishers, 1978.
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[15]	Combettes P L, Hirstoaga S A. Equilibrium programming in Hilbert spaces[J].J Nonlinear Convex Anal, 2005, 6: 117-136.

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平衡问题变分包含问题及不动点问题的二次极小化

doi: 10.3879/j.issn.1000-0887.2010.07.013

作者简介:
张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);李向荣(E-mail:majlee@polyu.edu.hk);陈志坚(E-mail:machanck@polyu.edu.hk).

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Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem

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平衡问题变分包含问题及不动点问题的二次极小化

doi: 10.3879/j.issn.1000-0887.2010.07.013

作者简介: 张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);李向荣(E-mail:majlee@polyu.edu.hk);陈志坚(E-mail:machanck@polyu.edu.hk).

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出版历程

Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem

计量

出版历程

目录

作者简介:
张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);李向荣(E-mail:majlee@polyu.edu.hk);陈志坚(E-mail:machanck@polyu.edu.hk).