In this paper, we introduce a new relaxed method for solving the split feasibility problem in Hilbert spaces. In our method, the projection to the halfspace is replaced by the one to the intersection of two halfspaces. We give convergence of the sequence generated by our method under some suitable assumptions. Finally, we give a numerical example for illustrating the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature.

In this paper, we introduce two new iterative algorithms, Halpern-Krasnosel'skiI-Mann iteration (HKM) and the Krasnosel'skiI-Mann-Halpern iteration (KMH) for fixed points of nonexpansive mappings. Under mild conditions, we proved the strong convergence theorems of the algorithms for fixed points of nonexpansive mappings in Hilbert spaces. Finally, we give a numerical example for illustrating the efficiency of the given algorithms in comparison with existing algorithms in the literatures.

In this paper, we investigate the generalized Halpern iteration for computing fixed points of nonexpansive mappings in Hilbert space setting, and prove the strong convergence under new control conditions on parameters. The convergence results generalize the existing ones in the literature. We also present a convergence rate analysis for the generalized Halpern iteration with a particular choice of parameters. Finally, we give an application to the split feasibility problem and two numerical examples for illustrating the performance of the algorithm.

In this paper, a question in the preliminary competition of the 12 th National College Mathematics Competition is discussed in a more general situation.The convergence of the sequence is proved, and the limit is obtained.

研究了强凸函数的一个不等式性质,该性质是对凸函数的Hermite-Hadamard不等式的加强.并给出其应用,得到了加强的指数平均不等式和对数平均不等式.

主要研究了分裂可行问题的1-范数正则化.首先利用1-范数正则化方法,将分裂可行问题转化为无约束优化问题.其次讨论了 1-范数正则化解的若干性质,并给出了求解1-范数正则化解的邻近梯度算法.最后通过数值试验验证了算法的可行性和有效性.

In this paper, we study the inertial relaxed CQ algorithm for solving a split feasibility problem in Hilbert spaces. For this algorithm, we establish two convergence theorems under two different conditions. The first condition is weaker than the existing condition, and the second condition is completely different from the existing one. Moreover the preliminary numerical experiment indicates that our proposed algorithms converge faster than the existing algorithms.

为了求解分裂可行问题,Yu等提出了一个球松弛CQ算法.由于该算法只需计算到闭球上的投影,同时不需要计算有界线性算子的范数,该算法是容易实现的.但是球松弛CQ算法在无穷维Hilbert空间中仅仅具有弱收敛性.首先构造了一个强收敛的球松弛CQ算法.在较弱的条件下,证明了算法的强收敛性.其次将该算法应用到一类闭凸集上的投影问题上.最后,数值试验验证了该算法的有效性.

为了得到信息系统的最小属性约简,提出了基于0-1规划的最小属性约简算法.首先,由区分矩阵定义了极小区分集的概念.其次,将信息系统的最小属性约简问题转化为0-1规划,从而给出了基于0-1规划的最小属性约简算法.再次,通过一个具体实例对该算法进行了说明.

计算信息系统的所有约简是一个典型的NP完全问题.不计算所有约简,而寻找所有约简中发生的可能性最大的约简,可以为属性约简提供了一种新的方法.首先,基于区分矩阵计算每个属性出现在约简中的概率;其次,将此概率作为属性的重要度,构建了最大可能约简算法,并进行了算法分析;最后,通过两个具体实例对该算法进行了说明.理论分析结果表明,本文的算法是有效可行的.

The relaxed CQ algorithm is a very efficient algorithm for solving the split feasibility problem (SFP) whenever the convex subsets involved are level subsets of given convex functions. It approximates the original convex subset by a sequence of half-spaces that overcomes the difficulties for calculating the projection onto original convex subsets. In this paper, we propose a new inertial relaxed algorithm in which we approximate the original convex subset by a sequence of closed balls instead of half spaces. Moreover, we construct a new variable step-size that does not need any prior information of the norm. We then establish the weak convergence of the proposed algorithm under two different assumptions. Experimental results in the LASSO and elastic net methods show that our algorithm has a better performance than other relaxed algorithms.

In this paper, we study the alternating CQ algorithm for solving the split equality problem in Hilbert spaces. It is, however, not easy to implement since its selection of the stepsize requires prior information on the norms of bounded linear operators. To avoid this difficulty, we propose several modified algorithms in which the selection of the stepsize is independent of the norms. In particular, we consider the case whenever the convex sets involved are level sets of given convex functions.

The split feasibility problem (SFP) is to find x is an element of C so that Ax is an element of Q, where C and Q are non-empty closed convex subsets in Hilbert spaces H-1 and H-2, respectively, and A is a linear bounded operator from H-1 to H-2. Byrne proposed an iterative method called the CQ algorithm that involves the orthogonal projections onto C and Q. However, the projections onto C and Q might be hard to be implemented in general. In this paper, we propose a ball-relaxed projection method for the SFP. Instead of half spaces, we replace C and Q in the proposed algorithm by two properly chosen closed balls C-k(b) and Q(k)(b). Since the projection onto the closed ball has closed form, the proposed algorithm is thus easy to be implemented. Under some mild conditions, we establish the weak convergence of the proposed algorithm to a solution of the SFP. As an application, we obtain new algorithms for solving the split equality problem. Preliminary numerical experiments show the efficiency of the proposed method.

In this paper, we are concerned with the split equality problem (SEP) in Hilbert spaces. By converting it to a coupled fixed-point equation, we propose a new algorithm for solving the SEP. Whenever the convex sets involved are level sets of given convex functionals, we propose two new relaxed alternating algorithms for the SEP. The first relaxed algorithm is shown to be weakly convergent and the second strongly convergent. A new idea is introduced in order to prove strong convergence of the second relaxed algorithm, which gives an affirmative answer to Moudafi's question. Finally, preliminary numerical results show the efficiency of the proposed algorithms.

本文基于Hellinger距离提出了一种判断矩阵排序方法,并研究了该排序方法的保序性、 置换不变性、相容性等性质.最后通过实例将基于Hellinger距离的排序方法与特征向量法、和积法以及方根法进行比较,理论分析和数值结果均表明该方法是有效的.

In the forced current commutation hybrid direct current (DC) circuit breaker based on full-controllable power electronic devices, the snubber capacitor discharge will affect the mechanical switch opening time in the process of auxiliary commutation circuit opening.When the action of the main circuit breaker is finished, the release of line energy just relies on the lightning arrester making the device damage-prone and affecting its useful life.The arrester investment cost is high and the time of energy dissipating is long.A forced current commutation hybrid DC circuit breaker is proposed, and its operating principle is analyzed.Finally, the feasibility of this scheme is verified by comparing with typical hybrid DC circuit breakers.Compared with the traditional forced current commutation hybrid DC circuit breaker based on full-controllable power electronic devices, the proposed scheme realizes the current bidirectional flow with only half the full-controllable power electronics devices.It can block the snubber capacitor discharging road without affecting the mechanical switch opening time, and reduce the line current to zero as soon as possible with a grounding diode circuit.

本文研究了广义近似空间的拓扑性质.首先证明了论域上任意二元关系均能诱导一个Alexandrov拓扑,并讨论了该拓扑的若干性质.其次给出了论域上两个不同二元关系诱导同一个拓扑的充分必要条件.最后在全体二元关系之集上定义了一个等价关系,并研究了等价类的结构.

在覆盖近似空间(U,C)中,基于最小描述定义了一种新的Zoom-in算子,并讨论了其性质.在论域U上,通过复合Zoom-in和Zoom-out算子,得到了具有对偶性的两对近似算子.同样在粒化论域C上,通过复合Zoom-out和Zoom-in算子,也得到了具有对偶性的两对近似算子.

In this paper, we consider some topological properties of generalized rough sets induced by binary relations and show that1. Any serial binary relation can induce a topology.2. Let R be a binary relation on a universe U. t(R) and e(R) denote the transitive closure and the equivalence closure of R, respectively. If R is a reflexive relation on U, then R and t(R) 'induce the same topology, i.e. T(R) = T(t(R)). The interior and closure operators of the topology T(R) induced by R are the lower and upper approximation operators a R1 and <(t(R))over bar>, respectively. Moreover, R(T(R)) = t(R), where R(T(R)) is the relation induced by the topology T(R).3. When R is a reflexive and symmetric relation, R and e(R) induce the same topology, i.e. T(R) = T(e(R)). The interior and closure operators of the topology T(R) induced by R are the lower and upper approximation operators e(R) and <(e(R))over bar>, respectively. Moreover, R(T(R)) = e(R).4. Based on the above conclusions, the notion of topological reduction of incomplete information systems is proposed, and characterizations of reduction of consistent incomplete decision tables are obtained. (C) 2013 Elsevier Inc. All rights reserved.

In the fuzzy probability space , the probabilistic fuzzy rough set model is established on the basis of fuzzy equivalent relation by means of fuzzy condition probability .The properties of probabilistic fuzzy upper and lower approximation operators are discussed .Finally , the calculation formulas of approximation accuracy and rough-ness measure of fuzzy sets are given .