Three-step iterations for nonexpansive mappings and inverse-strongly monotone mappings

This paper introduces a three-step iteration for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space. The authors show that the iterative sequence converges strongly to a common element of the two sets, which solves some variational inequality. Subsequently, the authors consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the corresponding results announced by Nakajo, Takahashi, and Toyoda. This research is supported by the National Natural Science Foundation of China under Grant No. 10771050.     

STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE MAPPING

This paper introduces a composite iteration scheme for approximating a fixed point of nonexpansive mappings in the framework of uniformly smooth Banach spaces and the reflexive Banach spaces which have a weakly continuous duality map, respectively, we establish the strong convergence of the composite iteration scheme. The results improve and extend those of Kim, Xu, Wittmann and some others.     

Inertial projection algorithms for convex feasibility problem

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.     

A new <Emphasis Type="Italic">ɛ</Emphasis>-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the ɛ-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new ɛ-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.     

基于新最速下降算法的自适应波束形成

针对阵列信号处理中自适应波束形成技术的抗干扰问题, 提出一种基于新的最速下降法的波束形成算法。新的最速下降法将多元二次凸优化问题转换为一元二次问题, 通过循环迭代的方式使求出的极值点向高维凸优化问题的极值点逼近, 最终使结果收敛到最优解。将这种算法应用于自适应波束形成, 提高自适应波束形成的收敛速度、抗干扰能力和低快拍下工作的能力。经过仿真验证, 与基于最小均方算法以及改进最小均方算法的波束形成方法进行比较, 所提出的波束形成算法具有抗强干扰、收敛速度快、能在低快拍条件下工作的优点。     

A general iterative method of fixed points for equilibrium problems and optimization problems

The purpose of this paper is to present a general iterative scheme as below:

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

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自适应混合混沌神经网络及其在TSP中的应用

为了进一步提高混沌神经网络的收敛效果,将T.Kwok和K.A.Smith所总结的内、外两类混沌神经网络相结合,并加入自适应方法,提出了自适应混合混沌神经网络。这种网络可以同时通过线性和非线性两种途径来改变网络能量函数进行搜索,这使得搜索过程具有更为丰富的动力学行为。同时由于自适应方法的引入,保证能量函数的变化在整个搜索过程中对动态方程有较强的作用,从而减少了网络收敛时的迭代步数。仿真研究表明,在求解TSP上,其效果优于随机混沌模拟退火网络。     

PDα-型分数阶迭代学习控制在Lp范数意义下的收敛性分析

针对一类分数阶线性系统,讨论了PD^α-型分数阶迭代学习控制算法的单调收敛性。首先,在Lebesgue^p(L^p)范数意义下,对一、二阶PD^α-型控制算法的单调收敛性进行理论分析,推导出其单调收敛的充分条件,并推广到N阶控制算法的情形;然后,对二者的收敛快慢进行了详细说明。结论表明,控制算法的收敛条件由学习增益和系统自身属性共同决定。仿真实验验证了理论的正确性和控制算法的可行性。     

The strong law of large numbers for pairwise NQD random variables

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz (1937), Jamison (1965), Matula (1992) and Wu (2001) from the independent identically distributed (i.i.d.) case to pairwise NQD sequences.     

LIMIT THEOREMS AND OPTIMAL DESIGN WITH ADAPTIVE URN MODELS

In this paper we study urn model, using some available estimates of successes probabilities, and adding particle parameter, we establish adaptive models. We obtain some strong convergence theorems, rates of convergence, asymptotic normality of components in the urn, and estimates. With these asymptotical results, we show that the adaptive designs given in this paper are asymptotically optimal designs.     

Hooke and Jeeves algorithm for linear support vector machine

Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine (SVM), at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves a...     

热工网络问题的大范围收敛解法

提出了热工网络问题的大范围收敛迭代解法，该算法避免了普通的直接差分方法所带来的稳定性困难，满足了过程仿真的收敛性与实时性的要求，为工业过程的建模与仿真提供了新的思路。本文还给出了一个仿真计算的例子。     

An affine scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming

This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.     

混合式能源-经济-环境系统模型构建方法论

目前,国际上用于温室气体(GHG,green house gas)减排影响研究的能源-经济-环境系统综合评价模型的主要建模思路,是在一个模型中同时融合自底向上的部门分析与自顶向下的宏观分析,构建混合模型.其中的难点是如何在一个模型里能够将2种思路协调一致.较详细地介绍构建混合模型的3种主流方法:1)在完整的自底向上的能源系统模型的基础上添加一个简单的宏观经济模块;2)在一个自顶向下的宏观经济模型之内,对能源生产部门采用自底向上的技术描述;3)将2种思路的模型使用几个变量联接起来构建混合模型,每个模型独自运转.通过这3种思路的对比分析,认为遵循第3种思路构建的混合模型应用范围更广泛,能够用于分析复杂的能源系统问题,例如GHG减排的影响及能源系统发展战略选择等.     

基于修正超指数迭代算法的双模式盲均衡算法仿真研究

收敛速度和剩余均方误差是评价盲均衡算法性能优劣的主要参数之一。超指数迭代盲均衡算法收敛速度快，但是，该算法对高阶QAM信号具有较大的剩余均方误差。针对数字无线电信道的盲均衡问题，提出了一种修正的超指数迭代盲均衡算法，该算法可校正无线电信道引入的载波相位旋转，并具有较快的收敛速度。在此基础上又提出了一种双模式盲均衡算法，该算法在收敛阶段采用修正的超指数迭代算法，之后根据某一切换准则，切换到判决导引算法，可有效减小超指数迭代算法对高阶信号的剩余均方误差。通过仿真证明了本算法的有效性。     

遥感影像K均值聚类中的初始化方法

遥感影像非监督分类对初始点十分敏感。以K均值(K-means)算法为例,利用各种遥感影像实验比较5种初始化方法(随机法、Forgy法、Macqueen法、Kaufman法、MaxMin法)对非监督分类方法的影响。实验表明,Kaufman法相对于其他方法更稳定,获得分类结果更优,适合于各种遥感影像的非监督分类,并指出可以通过采样来加快Kaufman法的运算速度。同时,通过实验分析了采样数和影像区域对初始化方法的影响。     

Super-resolution processing of passive millimeter-wave images based on adaptive projected Landweber algorithm

Passive millimeter wave(PMMW)images inherently have the problem of poor resolution owing to limited aperture dimension.Thus,efficient post-processing is necessary to achieve resolution improvement.An adaptive projected Laadweber(APL)super-resolution algorithm using a spectral correction procedure,which attempts to combine the strong points of all of the projected Landweber(PL)iteration and the adaptive relaxation parameter adjustment and the spectral correction method,is proposed.In the algorithm,the PL iterations are implemented as the main image restoration scheme and a spectral correction method is included in which the calculated spectrum within the passband is replaced by the known low frequency component.Then,the algorithm updates the relaxation parameter adaptively at each iteration.A qualitative evaluation of this algorithm is performed with simulated data as well as actual radiometer image captured by 91.5 GHz mechanically scanned radiometer.From experiments,it is found that the super-resolution algorithm obtains better results and enhances the resolution and has lower mean square error(MSE).These constraints and adaptive character and spectral correction procedures speed up the convergence of the Landweber algorithm and reduce the ringing effects that are caused by regularizing the image restoration problem.     

约束优化问题的一个超线性收敛的广义梯度投影法

对线性约束的非线性优化问题提出了一个新的广义梯度投影法，该算法我们采用了非精确线性搜索，并在每次迭代运算中运用了广义投影矩阵和变尺度方法的思想确定其搜索方向。在通常的假设条件下，证明了算法的整体收敛性和超线性收敛速度。     

Super-resolution processing of passive millimeter-wave images based on adaptive projected Landweber algorithm

Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive projected Landweber （APL） super-resolution algorithm using a spectral correction procedure, which attempts to combine the strong points of all of the projected Landweber （PL） iteration and the adaptive relaxation parameter adjustment and the spectral correction method, is proposed. In the algorithm, the PL iterations are implemented as the main image restoration scheme and a spectral correction method is included in which the calculated spectrum within the passband is replaced by the known low frequency component. Then, the algorithm updates the relaxation parameter adaptively at each iteration. A qualitative evaluation of this algorithm is performed with simulated data as well as actual radiometer image captured by 91.5 GHz mechanically scanned radiometer. From experiments, it is found that the super-resolution algorithm obtains better results and enhances the resolution and has lower mean square error （MSE）. These constraints and adaptive character and spectral correction procedures speed up the convergence of the Landweber algorithm and reduce the ringing effects that are caused by regularizing the image restoration problem.