WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES

In this paper,we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces.Then we study the weak convergence of the two iterative sequences.Our results improve and extend the results announced by many others.     

An extragradient method for relaxed cocoercive variational inequality and equilibrium problems

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 nonexpansivemappings, the set of an equilibrium problem and the set of solutions of the variational inequality problem 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, Takahashi and many others.     

仿射变换内点信赖域方法求解变分不等式问题

本文研究了求解非线性约束变分不等式问题(VIP)的一个新的算法.利用KKT条件的非光滑方程形式,得到了与VIP等价的简单约束优化问题.提出了求解VIP的一类结合回代线搜索技巧的仿射变换内点信赖域算法.在较弱的条件下证明了算法具有整体收敛性,进一步在某些正则条件下,证明了算法具有超线性收敛速度.     

具不等式约束变分不等式的信赖域算法

1　引　　言令Ｘ是Ｒｎ 中的非空闭凸集 ,Ｆ :Ｘ→Ｒｎ 是连续映射 ,〈· ,·〉表示Ｒｎ 中的内积 有限维变分不等式问题 (以下简称变分不等式问题 ,记为ＶＩＰ或ＶＩ(Ｘ ,Ｆ) ) :就是求ｘ ∈Ｒｎ,使ｘ ∈Ｘ且 ｘ ∈Ｘ ,〈Ｆ(ｘ ) ,ｘ -ｘ 〉≥ 0 . ( 1 )在Ｘ =Ｒｎ+ 的特殊情形下 ,( 1 )变为非线性互补问题 (记为ＮＣＰ或ＮＣＰ(Ｆ) ) :就是求ｘ ∈Ｒｎ,使ｘ ≥ 0 ,Ｆ(ｘ ) ≥ 0 ,且〈ｘ ,Ｆ(ｘ )〉 =0 . ( 2 )　　变分不等式长期以来一直用于阐述和研究经济学、控制论、交通运输等领域中出现的各种平衡模型 近二十年来 ,变分不等式及其…     

广义非凸变分不等式解的存在性与投影算法

本文运用Banach压缩映象原理和投影技巧研究一类新的广义非凸变分不等式问题解的存在唯一性,并在非凸集上建立一个逼近广义非凸变分不等式解的三步投影算法,在一定条件下证明了该投影算法所产生的迭代序列的收敛性.     

一类线性约束变分不等式问题的幂罚函数法

本文研究了一类线性约束变分不等式(Ⅵ)的幂罚函数法求解问题.利用Ⅵ的KKT条件,将Ⅵ转化为等价的混合互补问题和一个新的Ⅵ问题,并在一定条件下分析了解的存在性和唯一性.利用度理论证明了幂罚方程组解的存在性与唯一性.由以上结果最终证明了幂罚函数法的收敛性,即幂罚方程组的解收敛于Ⅵ问题的解.     

连续化方法求解变分不等式问题

利用变分不等式问题的KKT条件,给出了连续化方法求解变分不等式问题的一般框架,该框架包含了现存的几种连续方法;并给出一种求解的基本算法,证明了基本算法的可行性及算法的收敛性;最后用数值试验验证了算法的稳定性和有效性。     

有限个平衡问题与非扩张映象不动点问题的复合迭代方法

在Hilbert空间中引进并研究一种新的复合粘性迭代算法,借以寻求有限个平衡问题的公共解集与非扩张映象不动点集的一个公共元素.所得结果改进并推广了最近一些人的最新结果.     

求解单调变分不等式问题的一个连续型迭代方法

本文给出一个求解单调变分不等式问题的连续型迭代方法,对任意单调趋于零的正数序列和任意初始点,方法产生的迭代点列均收敛到所求变分不等式问题的一个解,且在适当条件下方法具有Q-超线性收敛率.数值试验结果进一步表明了所给方法的稳定性和有效性.     

A HYBRID METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEMS

§ 1　IntroductionThe problem of finding a point x* ∈S such that〈F(x* ) ,x -x* 〉≥ 0 for all x∈ S,(VIP)where S is a nonempty closed convex subset of Rn,F is a mapping from Rninto itself,and〈.,.〉denotes the inner productin Rn,is called the variational inequality problem and hasbeen widely used to study various equilibrium models arising in economic,operations re-search,transportation and regional sciences[1 ,2 ] .Many iterative methods for (VIP) havebeen developed,for example,project…     

AN ITERATIVE METHOD FOR SPLIT VARIATIONAL INCLUSION PROBLEM AND FIXED POINT PROBLEM FOR A FAMILY OF GENERALIZED ASYMPTOTICALLY NONEXPANSIVE SEMIGROUP

In this paper, strong convergence of an iterative sequence is proved, which computes an approximate solution of the set of solutions of split variational inclusion problem, the set of fixed points of a nonexpansive mapping and the set of common fixed points of a family of generalized asymptotically nonexpansive semigroup. Results obtained in this paper extend and unify the previously known results in the previous literatures.     

求单调变分不等式隐式方法的一个单调下降性质

1　引　　言变分不等式在数学规划中起着很重要的作用 ,许多研究者 [3 ]讨论了这一问题 .对于单调线性变分不等式问题 ,文 [4 -7]提出了几种投影收缩算法 ( PC) .最近文 [7]中研究了如下的一类变分不等式问题( VI)　　 u∈Ω ,　　 ( v -u) TF( u)≥ 0 ,　　 v∈Ω . ( 1 )其中Ω Rn 是一个闭凸集 ,F是 Rn到自身的连续单调映射 ,即F( u) -F( v) T( u -v)≥ 0 ,　　　 u,v∈ Rn. ( 2 )由 [1 ]知 ,对于任意的 β>0 ,变分不等式 ( 1 )等价于投影方程于是求解 ( 1 )即是寻求e( u,β)∶ =u -PΩ[u -βF( u) ]的零点 .本文中 Ω*表示 ( …     

一般单调变分不等式的一个改进的预估-校正算法

最近何炳生等提出了解大规模单调变分不等式的一种预估-校正算法,然而,这个方法在计算每一个试验点时需要一次投影运算,因而计算量较大．为了克服这个缺点,我们提出了一个解一般大规模g-单调变分不等式的新的预估-校正算法,该方法使用了一个非常有效的预估步长准则,每个步长的选取只需要计算一次投影,这将大大减少计算量．数值试验说明我们的算法比最新文献中出现的投影类方法有效．     

APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

In this paper, a convex feasibility problem is considered. We construct an iterative method to approximate a common element of the solution set of classical variational inequalities and of the fixed point set of a strict pseudocontraction. Strong convergence theorems for the common element are established in the framework of Hilbert spaces.     

HYBRID ITERATION METHOD FOR GENERALIZED EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

In this paper, weak and strong convergence theorems are established by hybrid iteration method for generalized equilibrium problem and fixed point problems of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. The results presented in this paper partly extend and improve the corresponding results of the previous papers.     

求解变分不等式问题的一个递推算法的一个注

本文改进了[3]中的一个基本不等式和原算法，从而提高了数值计算的效率,而且在新算法的收敛性分析中去掉了变分不等式问题的单调性条件．     

求解盒子形区域上变分不等式的逐次逼近类Broyden算法

In this paper, a successive approximation Broyden-like method is presented for the box constrained variational inequality problems based on its equivalent nonsmooth equations. The global convergence of the algorithm is obtained under suitable conditions. Numerical results are also reported.     

非扩张半群的变分不等式的不动点解的粘性逼近方法

本文研究了非扩张半群的变分不等式的不动点解的迭代算法.利用变分不等式与不动点问题的解的关系,结合粘性逼近方法,建立了非扩张半群的不动点的两步迭代格式,证明了该方法所得到的迭代序列在一定条件下的强收敛性,并收敛于某变分不等式的唯一解.     

变分不等式问题的全局收敛性算法

本文给出了带一般凸约束的变分不等式问题的算法,并在多种线性搜索下证明了算法的全局收敛性。     

THE SCHWARZ ALTERNATING METHOD FOR A FOURTH-ORDER VARIATIONAL INEQUALITY

In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.