A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.

Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

Existence and Uniqueness of Analytic Solutions of Systems of Iterative Functional Equations

Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and f|D ° is analytic}. Suppose G,H: D 2n+1 →C are continuous maps (n≥2), and G|(D 2n+1 ) °, H|(D 2n+1 ) ° are analytic. In this paper, we study the system of iterative functional equationsG(z,f(z),…,f n(z), g(z),…,g n(z))=0, H(z,f(z),…,f n(z), g(z),…,g n(z))=0, for any z∈D,and give some conditions for the system of equations to have a solution or a unique solution in A(D,D) ×A(D,D).

Iterative analytic extension in tomographic imaging

If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.

Operator Equation and Application of Variation Iterative Method

In this paper, we study some semi-closed 1-set-contractive operators A and investigate the boundary conditions under which the topological degrees of 1-set contractive fields, deg (I-A, Ω, p) are equal to 1. Correspondingly, we can obtain some new fixed point theorems for 1-set-contractive operators which extend and improve many famous theorems such as the Leray-Schauder theorem, and operator equation, etc. Lemma 2.1 generalizes the famous theorem. The calculation of topological degrees and index are important things, which combine the existence of solution of for integration and differential equation and or approximation by iteration technique. So, we apply the effective modification of He’s variation iteration method to solve some nonlinear and linear equations are proceed to examine some a class of integral-differential equations, to illustrate the effectiveness and convenience of this method.

改进迭代贪婪算法求解可重入流水车间调度问题

可重入混合流水车间是在混合流水车间的基础上增加了可重入特性,具有更高的调度复杂性。为了求解可重入混合流水车间调度问题,首先建立了调度优化模型,优化目标为最小化最大完工时间,然后提出一种带精英调整的学习型迭代贪婪算法(LIG-EA)。LIG-EA算法采用基于工件的编码方式,对重组后的染色体进行解码。种群分为精英个体和普通个体两部分,对精英个体进行精英破坏重建和基于关键工件的染色体调整,对普通个体进行学习机制的构建和普通个体的破坏重建。为提高初始种群质量,采用NEH启发式算法进行种群初始化,并针对可重入混合流水车间的重入特性,在重建操作中增加了插入有效性判断,提高了算法的运行速度。通过大量实验表明LIG-EA算法能够有效求解可重入混合流水车间调度问题。

Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.

HAUSDORFF CENTRED MEASURE OF NON-SYMMETRY CANTOR SETS

Let 0<λ_1,λ_2<1 and 1-λ_1-λ_2≥max｛λ_1,λ_2｝.Let ~K(λ_1,λ_2) be the attractor of the iterated function system ｛φ_1,φ_2｝on the line,where φ_1(x)=λ_1x and φ_2(x)=1-λ_2+λ_2x,x∈R.~K(λ_1,λ_2) is called a non-symmetry Cantor set. In this paper,it is proved that the exact Hausdorff centred measure of K(λ_1,λ_2) equals 2s(1-λ)s,where λ=max｛λ_1,λ_2｝ and s is the Hausdorff dimension of K(λ_1,λ_2).

CONTINUITY OF JULIA SET FOR A FAMILY OF ENTIRE FUNCTIONS

Based on the work of McMullen about the continuity of Julia set for rational functions, in this paper, we discuss the continuity of Julia set and its Hausdorff dimension for a family of entire functions which satisfy some conditions.

"MANDELBROT SET" FOR A PAIR OF LINEAR MAPS: THE LOCAL GEOMETRY

We consider the iterated function system {λz-1, λz + 1} in the complex plane, for A in the open unit disk. Let M be the set of λ such that the attractor of the IFS is connected. We discuss some topological and geometric properties of the set M and prove a new result about possible corners on its boundary. Some open problems and directions for further research are discussed as well.

A Note on Invariant Sets

The lower bound of Hausdorff dimension of the invariant set is given.

Set-Valued Non-Linear Random Implicit Quasivariational Inclusions

In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.

近零碳排放园区综合评价指标与方法

针对当前近零碳园区综合评价指标体系缺失的问题,首先,构建了包含7项一级指标和20项二级指标的评价体系,并明确了指标内涵及计算方法;其次,通过主客观结合的集值迭代–批判法(Set value iteration,SVI;Criteria importance through intercrieria correlation,CRITIC)确定指标主客观权重,根据矩阵论基本理论计算各指标组合权重,从而避免了单一赋权的片面性;然后,分别研究定性和定量指标的模糊综合计算方式,构建了综合评价模型;最后,以某近零碳园区运行数据为例进行了验证。验证结果表明,所提方法能较为全面地对近零碳排放园区建设情况进行科学评价。

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

引入改进迭代局部搜索的灰狼算法及应用

针对标准灰狼算法(GWO)收敛速度慢,易陷入局部最优等缺点,提出一种引入改进迭代局部搜索的灰狼算法(IGWO)。首先,通过佳点集策略增强初始种群的均匀性与多样性;其次,采用双收敛因子,收敛因子基于种群位置非线性自适应更新,在种群寻优全期平衡全局勘探与局部开发能力;再次,在种群位置更新公式引入欧氏动态权重与莱维飞行策略,提升寻优精度,并帮助种群跳出局部最优值;最后,引入改进迭代局部搜索,使算法的搜索能力更加灵活,帮助算法加速收敛。通过10个基准测试函数的仿真分析及种群寻优平衡性对比,证明了IGWO具有更优的寻优精度、稳定性及收敛速度,随后将IGWO应用于工程优化问题中,相比GWO、GJO、WOA、HSSAHHO、SCHOA、NCPGWO、DSFGWO 7种算法,适应度分别优化了3.25%、27.2%、28.9%、3.15%、3.04%、0.23%、0.07%,证实了在工程应用中的可行性和有效性。

基于佳点集人工鱼群的点云配准算法

针对点云配准迭代最近点(iterative closest point,ICP)算法对点云的初始位置姿态有较高的要求且易陷入局部最优的问题,文章提出一种基于佳点集人工鱼群的点云配准算法。首先采用佳点集方法对人工鱼群初始化,解决人工鱼群因初始种群分布不均而陷入局部最优的问题,并通过下采样与三维尺度不变特征变换(3D scale invariant feature transform,3D SIFT)特征点提取简化点云;然后采用快速点特征直方图(fast point feature histogram,FPFH)特征描述解求点云间的对应点对并剔除错误对应点对,通过佳点集人工鱼群算法寻优刚性变换的6个参数完成粗配准;最后使用ICP算法完成精配准。实验选取斯坦福大学提供的Bunny、Dragon和Happy Buddha 3组测试数据集进行配准;结果表明,该文算法收敛速度快,能为ICP算法提供良好的初始位姿避免其陷入局部最优。