拟非扩张多值映像的分层最优化问题

在Hilbert空间中引入拟非扩张多值映像的概念,讨论拟非扩张多值映像的分层最优化问题的迭代算法,在适当的条件下证明此迭代序列的强收敛性.文中所得到的结果,推广并改进了最近一些人所发布的新结果.     

带扰动映像的广义平衡问题和不动点问题的混合粘性逼近问题

引入一个用于寻求带扰动映像的广义平衡问题解集以及可数无穷多非扩张映像之族公共不动点集的公共解的新的迭代算法. 证明了由此算法生成的序列的强收敛性. 所得的结果推广改进了先前许多作者的结果.     

一类变分不等式和非扩张映像不动点问题的一个迭代算法

该文提出了关于含松弛强制映像变分不等式和不动点问题解的一个投影迭代算法,所得结果改进和推广了目前一些作者的研究结果.     

非扩张映像不动点新的简单逼近算法

提出了一个简单的非扩张映像不动点的逼近算法,该算法通过非迭代的逼近序列来实现.从算法的复杂性来看,提出的算法比经典的Mann迭代算法、Ishikawa迭代算法和Halpern迭代算法更简单.提出的算法紧密联系着非扩张映像不动点的存在性,因此,还得到了非扩张映像的新不动点定理, 拓展和改进了经典的Goebel-Kirk,Kim-Xu等作者的结果.     

拟非扩张映像族的公共不动点的迭代方法

引入了修正的杂交投影迭代算法,用来构造Hilbert空间中拟非扩张映像族的公共不动点.使用新的算法证明了几个强收敛定理.新算法的优点是不要求映像具有次闭性质.     

平衡问题和拟φ-渐近非扩张映像的强收敛定理

在自反、严格凸、光滑的Banach空间中,设计了一种修正的混合投影迭代算法用来构造平衡问题与拟φ-渐近非扩张映像的不动点问题的公共元,并利用广义投影算子和K-K性质证明了此迭代算法生成的序列强收敛于这两个问题的公共元.所得结果是近期相关结果的改进和推广.     

Hilbert空间中k—严格伪压缩映像不动点的迭代算法

给出了Hilbert空间中k-严格伪压缩映像不动点的一个迭代算法,并利用所给出的算法证明了一个强收敛定理.     

拟-Φ-渐近非扩张映像不动点的迭代

给出了Banach空间中拟Φ-渐近非扩张映像族公共不动点的一个修正的迭代算法,并利用所给出的算法证明了一个强收敛定理.     

渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题

研究了Banach空间中渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题,改进和发展了张石生教授等人的相应结果.     

严格拟伪压缩映像族的复合迭代算法

在Hilbert空间中设计了一种关于严格拟伪压缩映像族的复合迭代算法,并利用度量投影法证明了严格拟伪压缩映像族的公共不动点的强收敛定理,所得结果改进和推广了一些最新文献的相关结果.     

Hilbert空间上新的变分不等式问题和不动点问题的粘性迭代算法

本文在Hilbert空间上引入了一个新的粘性迭代算法,找到了关于两个逆强单调算子的变分不等式问题的解集与非扩张映射的不动点集的公共元.通过修改的超梯度算法,得到了强收敛定理,也给出了一个数值例子.所得结果改进了许多最新结果.     

A new iterative algorithm for the variational inequality problem over the fixed point set of a firmly nonexpansive mapping

Many problems to appear in signal processing have been formulated as the variational inequality problem over the fixed point set of a nonexpansive mapping. In particular, convex optimization problems over the fixed point set are discussed, and operators which are considered to the problems satisfy the monotonicity. Hence, the uniqueness of the solution of the problem is not always guaranteed. In this article, we present the variational inequality problem for a monotone, hemicontinuous operator over the fixed point set of a firmly nonexpansive mapping. The main aim of the article is to solve the proposed problem by using an iterative algorithm. To this goal, we present a new iterative algorithm for the proposed problem and its convergence analysis. Numerical examples for the proposed algorithm for convex optimization problems over the fixed point set are provided in the final section.     

Approximating a Zero of Sum of Two Monotone Operators Which Solves a Fixed Point Problem in Reflexive Banach Spaces

Abstract

The purpose of this paper is to introduce an iterative method for approximating a point in the set of zeros of the sum of two monotone mappings, which is also a solution of a fixed point problem for a Bregman strongly nonexpansive mapping in a real reflexive Banach space. With our iterative technique, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a variational inclusion problem for sum of two monotone mappings and the set of solutions of a fixed point problem for Bregman strongly nonexpansive mapping. We give applications of our result to convex minimization problem, convex feasibility problem, variational inequality problem, and equilibrium problem. Our result complements and extends some recent results in literature.     

Banach空间中非膨胀映象和α-逆强增生算子的强收敛性

在2-一致光滑的Banach空间中,引入一种新的迭代算法研究非膨胀映象的不动点集与α-逆强增生算子的变分不等式解集的公共元素,并获得了迭代算法的强收敛性定理.而且应用这些结果考虑了非膨胀映象和严格伪压缩映象公共不动点的收敛性问题.     

A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping

The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space.     

Hilbert空间中关于变分不等式问题和不动点问题的粘性隐式中点算法

该文在Hilbert空间中研究了关于两个逆强单调算子的一般变分不等式问题和非扩张映射的不动点问题的粘性隐式中点算法,用修改的超梯度方法,在对参数作适当的限制下,得到了强收敛定理,所得结果推广和提高了许多最新文献中的相应结果.     

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.     

Hilbert空间中混合平衡问题与非扩张半群的强收敛定理

在Hilbert空间中引进并研究了一种新的迭代算法,借以寻求混合平衡问题解集与非扩张半群不动点集的一公共元.所得到的结果,推广并改进了最近一些人所发布的新结果.     

A hybrid extragradient method for general variational inequalities

In this paper, we introduce and study a hybrid extragradient method for finding solutions of a general variational inequality problem with inverse-strongly monotone mapping in a real Hilbert space. An iterative algorithm is proposed by virtue of the hybrid extragradient method. Under two sets of quite mild conditions, we prove the strong convergence of this iterative algorithm to the unique common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality problem, respectively. L. C. Zeng’s research was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), and Science and Technology Commission of Shanghai Municipality grant (075105118). J. C. Yao’s research was partially supported by a grant from the National Science Council of Taiwan.