Self-Adaptive Algorithms for the Split Common Fixed Point Problem of the Demimetric Mappings

The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces. Moreover, our algorithm does not need any prior information of the operator norm. Weak and strong convergence theorems are given under some mild assumptions. The results in this paper are the extension and improvement of the recent results in the literature.

基于ICA Fixed-Point算法的信号图像分析

从ICA算法的基准点出发,探讨了固定点算法中寻找W叠代公式的原理和方法,对分离一个独立成分和分离n个独立成分的运算方法进行了推导和分析;模拟试验表明:逐一分离的效果较好。

An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H;: Ux = x} and F（T） = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.

Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups

Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

Stochastic Approximation Method for Fixed Point Problems

We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.

具有限族半压缩映射的修正惯性同步算法的强收敛性

研究一个新的具有限族半压缩映射的修正惯性同步算法。在希尔伯特空间框架下,结合压缩映射,在适当的条件下建立一些强收敛定理。同时,给出了一个数值例子来说明所建议的算法的有效性。

结合载客热点和POI的出租车停车位划定方法

针对出租车随意停靠造成城市交通拥堵甚至交通事故的问题,利用成都实际区域的出租车GPS(Global Position System)数据和爬取的POI(Point of Interest)数据,使用DBSCAN(Density-Based Spatial Clustering of Application with Noise)聚类算法对上下客点进行聚类,得到出租车的载客热点,根据POI的类型划定载客热点区域的类型,对出租车不同时间的出行需求进行分析,进而划分出出租车的固定停车区域。研究结果表明,出租车固定停车区域的设定与出行者的出行需求有关,即将固定停车区域设置在出行者出行需求多的区域,可以满足出行者的不同出行需求。结合出租车载客热点和爬取POI数据划定固定停车区域的方法具有较高的实用性,可为城市交通安全方面提供理论和现实意义。

An N/4 fixed-point duality quantum search algorithm

Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.

A PRIMAL-DUAL FIXED POINT ALGORITHM FOR MULTI-BLOCK CONVEX MINIMIZATION

We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.

Global optimality condition and fixed point continuation algorithm for non-Lipschitz ?_p regularized matrix minimization

Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.

基于Isight的增程式电动汽车定点控制策略优化

基于专家经验和工程经验制定的传统规则能量管理策略并不能适应当前增程式汽车复杂的行驶工况,为了更加精确地控制增程式汽车,使其获得更好的燃油经济性,考虑到增程器中发动机定点控制策略的发动机工作点切换规则影响,采用Cruise建立整车模型、Isight对其参数进行优化的方式探究发动机工作点切换规则对油耗的影响,比较其百公里油耗。研究结果表明,优化后NEDC工况、WLTC工况、混合工况的百公里燃油消耗量分别降低了3.51%、7.3%、8.5%,为增程式汽车定点控制策略优化提供了一种新方法,并验证了其可行性。

Banach空间中可数拟-φ-非扩张映像族的公共不动点的收敛定理

在某些Banach空间中针对一类闭的拟-φ-非扩张映像的可数无限族,修正经典的正规Mann迭代算法以达到强收敛的目标,所得结果改进并扩展了Matsushita和Takahashi等人的相关结果.

变分不等式问题和不动点问题的公共元的新投影算法

在Hilbert空间中针对求解变分不等式问题和不动点问题的公共元给出一种新的投影算法,在适当的条件下,采用粘性逼近方法和投影算子的技巧证明了由该算法生成的迭代序列强收敛于伪单调变分不等式解集和两个半压缩映射公共不动点集的公共元。最后,给出数值实验说明该算法的有效性优于已有算法。

一种基于峭度的一单元ICA-R固定点算法

一单元参考独立成分分析是一种有效的利用先验信息抽取一个期望源信号的方法。以峭度的绝对值为对比函数推导出一种一单元ICA-R固定点算法,该算法避免了对比函数二阶导数的计算,简化了运算复杂度,比基于峭度的牛顿快速算法有更快的收敛速度。通过计算机模拟实验验证了算法的有效性。

基于MNC-FastICA算法的稳健自适应波束形成

针对导向向量失配的稳健自适应算法主要是基于导向向量不确定集约束,但是其约束参数往往难以确定,提出了基于修正的非圆复值快速不动点算法(MNC-FastICA)的波束形成方法,通过盲分离得到的分离矩阵来构造波束权向量,并对由此产生的信源幅相模糊进行校正。该方法不必预先估计信号来波方向,避免了传统方法中来波方向估计不准引起的期望信号的导向向量失配;对于阵列通道幅相误差导致的导向向量失配,该方法对其不敏感,不必对阵列进行校正。仿真实验与最差性能最佳化(WCPO)等经典方法作了性能对比,结果验证了该算法的有效性和稳健性。

一种WTMSST结合自适应参数VMD的滚动轴承故障诊断

针对现有轴承故障诊断中常用的时频分析方法存在变换系数在时频平面上分布相对离散,时频谱能量模糊等共性问题,提出了一种基于小波变换的时间重分配多同步压缩变换(WTMSST)结合经蜣螂算法(DBO)优化变分模态分解(VMD)的滚动轴承故障诊断方法。该方法采用了一种根据重分配同步压缩变换(WTSST)优化的WTMSST算法,通过固定点迭代减少了在强频率变化下的群延迟,然后通过以最小包络熵为适应度的DBO算法优化VMD输入参数,根据峭度重构信号后,运用WTMSST进行故障特征提取。采用凯斯西储大学的数据集进行测试,验证该法准确描述了信号的冲击特征,并证明其较过往处理方式具有更好的性能。

自由边界问题的自适应预测-校正算法

对一类自由边界问题,提出了基于线性互补问题的自适应预测-校正算法.用有限差分对微分模型离散化后得到一个正定线性互补问题,该问题等价于一个不动点问题,从而得到求解线性互补问题的自适应预测-校正算法.用正定性及投影基本性质可证明算法收敛性.给出了具体的算法过程,数值结果表明了算法的可行性和有效性.

新CICA一单元ICA-R固定点算法

一单元参考独立成分分析是一种有效地利用先验信息抽取一个期望源信号的方法。针对基于峭度的快速算法抽取正确率较低的缺点,在两种常用近似性量度下对快速算法进行了理论分析,指出该方法抽取正确率低的原因,通过避免不等式约束失效的方法,基于新CICA提出了一种一单元ICA-R固定点算法。大量计算机模拟实验表明所提算法抽取性能和快速算法相当,但具有更快的收敛速度和更高的抽取正确率。