非自反Banach空间中的度量投影

该文给出非自反Banach空间中一类超平面上度量投影的表达式．在近严格凸Banach空间中,研究了它们的连续性．对于对偶Banach空间X*,给出弱*闭子集上度量投影的一些连续性结果．     

Banach空间中极大单调算子的一个邻近点算法

设E是Banach空间,T∶E→2E*是极大单调算子,T-10≠ф.令x0∈E,yn=(J λnT)-1xn en,xn 1=J-1(αnJxn (1-αn)Jyn),n0,λn>0,αn∈[0,1],文章研究了{xn}收敛性.     

On Diagonal Subdifferential Operators in Nonreflexive Banach Spaces

Consider a real-valued bifunction f defined on C ×C, where C is a closed and convex subset of a Banach space X, which is concave in its first argument and convex in its second one. We study its subdifferential with respect to the second argument, evaluated at pairs of the form (x,x), and the subdifferential of − f with respect to its first argument, evaluated at the same pairs. We prove that if f vanishes whenever both arguments coincide, these operators are maximal monotone, under rather undemanding continuity assumptions on f. We also establish similar results under related assumptions on f, e.g. monotonicity and convexity in the second argument. These results were known for the case in which the Banach space is reflexive and C = X. Here we use a different approach, based upon a recently established sufficient condition for maximal monotonicity of operators, in order to cover the nonreflexive and constrained case (C ≠ X). Our results have consequences in terms of the reformulation of equilibrium problems as variational inequality ones.     

极大单调算子的一个邻近点算法

设E是自反的Banach空间,T∶E→2E是极大单调算子.T-10≠.令x0∈E,yn=(J λnT)-1xn en,xn 1=J-1(αnJxn (1-αn)Jyn),n≥0,λn>0,αn∈[0,1],本文研究了{xn}收敛性.     

Inexact Proximal Point Methods for Equilibrium Problems in Banach Spaces

We introduce two inexact proximal-like methods for solving equilibrium problems in reflexive Banach spaces and establish their convergence properties, proving that the sequence generated by each one of them converges to a solution of the equilibrium problem under reasonable assumptions.     

On Inclusions with Monotone-Type Mappings in Nonreflexive Banach Spaces

Journal of Optimization Theory and Applications - We are concerned in this article with the existence of solutions to inclusions containing generalized pseudomonotone perturbations of maximal...     

Banach空间中解变分包含问题的超松弛临界点算法

把Verma关于解变分包含问题的超松弛临界点算法(over-relaxed proximalpoint algorithm)从Hilbert空间扩展为q一致光滑Banach空间.并且导出了更为广义的超松弛临界点算法,在较弱的条件下证明了它的收敛性质.因此,研究结果可以应用于L~p,W~(m,p)(Ω)(p1)等空间.     

Regularization Proximal Point Algorithm for Common Fixed Points of Nonexpansive Mappings in Banach Spaces

We study the strong convergence of a regularization proximal point algorithm for the problem of finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and uniformly smooth Banach space E.     

Strong Convergence of an Inexact Proximal Point Algorithm for Equilibrium Problems in Banach Spaces

We develop an inexact proximal point algorithm for solving equilibrium problems in Banach spaces which consists of two principal steps and admits an interesting geometric interpretation. At a certain iterate, first we solve an inexact regularized equilibrium problem with a flexible error criterion to obtain an axillary point. Using this axillary point and the inexact solution of the previous iterate, we construct two appropriate hyperplanes which separate the current iterate from the solution set of the given problem. Then the next iterate is defined as the Bregman projection of the initial point onto the intersection of two halfspaces obtained from the two constructed hyperplanes containing the solution set of the original problem. Assuming standard hypotheses, we present a convergence analysis for our algorithm, establishing that the generated sequence strongly and globally converges to a solution of the problem which is the closest one to the starting point of the algorithm.     

Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces

Two strong convergence theorems for a proximal method for finding common zeroes of maximal monotone operators in reflexive Banach spaces are established. Both theorems take into account possible computational errors.     

A Generalized Proximal Point Algorithm and Implicit Iterative Schemes for a Sequence of Operators on Banach Spaces

The aim of this paper is to obtain weak convergence of an iterative scheme generated by a sequence of accretive operators defined on a real Banach space, which is a generalization of the result given by Kamimura and Takahashi (J. Approx. Theory 106:226–240, 2000). We also show several applications to the implicit iterative schemes with the Yosida approximations and with the W-mappings generated by a sequence of nonexpansive mappings.     

Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces

In this work, we consider two classes of non-self-mappings, which are called proximal weakly contractive and proximal nonexpansive mappings, and study the existence of solutions of a minimization problem. Existence results of best proximity points for these two classes of non-self-mappings in metric and Banach spaces are also obtained.     

Inexact Proximal Point Methods in Metric Spaces

We study the local convergence of a proximal point method in a metric space under the presence of computational errors. We show that the proximal point method generates a good approximate solution if the sequence of computational errors is bounded from above by some constant. The principle assumption is a local error bound condition which relates the growth of an objective function to the distance to the set of minimizers introduced by Hager and Zhang (SIAM J Control Optim 46:1683–1704, 2007).     

A Fixed Point Theorem for Increasing Operators in Banach Spaces

ＡＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｅｍｆｏｒＩｎｃｒｅａｓｉｎｇＯｐｅｒａｔｏｒｓｉｎＢａｎａｃｈＳｐａｃｅｓ￥ＬｉＦｅｎｇｙｏｕ李凤友（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＮｏｍａｌｕｎｉｖｅｒｓｉｔｙ，３０００７３．Ｐ．Ｒ...     

Least Square Control Problems in Nonreflexive Spaces

We consider a control problem in a Banach space with a bounded observer, but an unbounded controller which takes values in the extrapolated Favard class. A least square regulator problem can be formulated if the observer and the admissible controls take values in Hilbert spaces. We prove that for this type of LQR-problem the value function is given by a Riccati operator, and that a bounded state feedback based on the Riccati operator yields the optimal control. April 30, 1999     

Banach空间上的不连续映射的不动点定理

本文把著名的Ｓｃｈａｕｄｅｒ定理推广到不连续映射的情形，主要的结果表明对任一Ｂａｎａｃｈ空间中的任一给定的紧凸子集上的任一自映射，可以在紧凸集上找一点ｘ，使‖ｘ－ｆ（ｘ）‖不超过函数的固定的不连续测量，这一结果推广了Ｓｃｈａｕｄｅｒ定理和文［１］的结果     

Banach空间中一类映像的三重迭代法

利用赋范线性空间X的凸性模定义,以及凸性模的单调性及半紧性条件,研究了渐近非扩张映射不动点的三步迭代法.减弱了许多条件,从而推广了同类问题的某些结果.     

Proximal Point Algorithm for Quasi-Convex Minimization Problems in Metric Spaces

In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove Δ-convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.     

关于非扩张映射的不动点问题的粘性迭代算法的强收敛定理

该文首先研究吸引非扩张映射的性质,然后在一致光滑Banach空间里,用这些性质研究两个非扩张映射的不动点问题的粘性迭代算法.作为应用,在Banach空间或Hilbert空间里,得到了关于变分不等式问题,不动点问题和均衡问题的强收敛定理.所得结果提高和推广了许多最近的相关结果.