A New Class of Nonlinear Conjugate Gradient Methods with Global Convergence Properties

非线性共轭梯度法由于其迭代简单和储存量小,且搜索方向不需要满足正割条件,在求解大规模无约束优化问题时占据及其重要的地位.提出了一类新的共轭梯度法,其搜索方向是目标函数的下降方向.若假设目标函数连续可微且梯度满足Lipschitz条件,线性搜索满足Wolfe原则,讨论了所设计算法的全局收敛性.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

GLOBAL CONVERGENCE OF THE GENERAL THREE TERM CONJUGATE GRADIENT METHODS WITH THE RELAXED STRONG WOLFE LINE SEARCH

The global convergence of the general three term conjugate gradient methods with the relaxed strong Wolfe line search is proved.

ON THE GLOBAL CONVERGENCE OF CONJUGATE GRADIENT METHODS WITH INEXACT LINESEARCH

In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.

A Scaled Conjugate Gradient Method Based on New BFGS Secant Equation with Modified Nonmonotone Line Search

In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.

On-line血液透析滤过应用高钠及超滤曲线对血压的影响

目的研究on-lineHDF时应用高钠及超滤曲线是否对血压有影响。方法回顾性分析我院10名终末期肾衰竭(ESRD)患者的60例次HDF治疗,根据应用高钠与超滤曲线与否分成A、B两组(两组各30次),对两组患者行HDF时的1h、2h、3h、4h及最低血压进行比较。结果A、B组患者在其1h、2h、3h、最低血压比较差异有显著性,P<0.05。在其4h血压比较差异无显著性,P>0.05。结论结合高钠及超滤曲线可使患者进行HDF时血压平稳,比单纯行HDF的血流动力学更稳定。

A CLASSOF NONMONOTONE CONJUGATE GRADIENT METHODSFOR NONCONVEX FUNCTIONS

This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases

A projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem

Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

A hybrid conjugate gradient method for optimization problems

A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits an important property of the well known PRP method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening;ii) The scalar holds automatically;iii) The global convergence with some line search rule is established for nonconvex functions. Numerical results show that the method is effective for the test problems.

Multi-component joint inversion of gravity gradient based on fast forward calculation

With the development of gravity gradient full tensor measurement technique,three-dimensional( 3D) inversion based on gravity gradient tensor can provide more accurate information. But the forward calculation of 3D full tensor sensitivity matrix is very time-consuming,which restricts its development and application.According to the symmetry of the kernel function,the authors reconstruct the underground source of geological body to avoid repeat computation of the same value,and work out the corresponding relationship between the response of geological body to the observation point and the response of reconstructed geological body to the observation point. According to the relationship,rapid calculation of full tensor gravity sensitivity matrix can be achieved. The model calculation shows that this method can increase the speed of 30-45 times compared with the traditional calculation method. The sensitivity matrix is applied to the multi-component inversion of gravity gradient. The application of this method on the measured data provides the basis for the promotion of the method.

一种基于线性零磁场的动脉血管扫描成像方法仿真

基于磁电耦合效应的血流检测及血管成像是实现心血管疾病早期诊疗的有效方法之一。该文基于磁场与血流耦合电效应,设计一种用于动脉血管扫描成像的组合线圈结构,产生带有零磁场线(FFL)区域的线性梯度磁场;在此结构的基础上,通过控制激励电流驱动FFL实现成像区域双向扫描;结合卷积神经网络(CNN)实现磁电耦合信号与血管信息的非线性映射,进而提出一种基于线性零磁场的动脉血管扫描成像新方法。采用多物理场仿真软件COMSOL对基于线性零磁场的血管扫描成像方法进行建模,求解磁电耦合信号,验证了所提出方法的合理性和有效性。结果表明,线性梯度磁场模式下的磁电耦合信号含有血管位置、半径等信息;CNN重建血管位置误差平均值为1.5694 mm,重建血管半径的方均误差(MSE)和相关系数(CC)平均值分别为0.0548和0.9870。研究结果可用于血管成像装置设计及后续相关临床应用提供研究支撑。

Modification Method of Lightning Shielding Angle Calculation for Transmission Lines in Mountain Areas

Shielding angle is one of the main factors influencing lightning performance of transmission lines,which always stays in the focus of the design and the evaluation of lightning protection.A formula for the improved shielding angle is proposed for evaluating the lightning performance in different terrains.The digital elevation model(DEM) is used to obtain the micro-topography data,such as the slope gradient,slope aspect,etc.The following results are obtained by analyzing the influence of topography factors on the improved shielding angle:(1) improved shielding angle non-linearly increases with the increase of the slope gradient and the slope aspect,(2) improved shielding angle is more sensitive to the slope gradient than to the slope aspect,(3) the improved shielding angle in the mountain terrains is much greater than the designed shielding angle.This may be the reason why the designed shielding angle is limited into the rational range,while the shielding faults occur frequently.

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUTSUFFICIENT DECREASE CONDITION

Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.

广州市城市轨道交通车站及线路分类

城市轨道交通在带动沿线经济发展的同时,也出现了与城市功能发展不协调、运力资源利用不充分不平衡的问题。基于广州市12条城市轨道交通线路185个车站周边地区的人口、用地、客流量、POI、道路网和公共汽车交通设施等5类66项指标数据,采用K-均值聚类方法将城市轨道交通车站划分为极端就业型、高度开发偏就业型、高度开发偏居住型、中度综合开发型、低度开发偏就业型、低度开发偏居住型6类。以不同城市轨道交通线路中各类型车站比例和运营指标数据为依据,将城市轨道交通线路划分为梯度平衡型、职住极化型、功能混合型、客流不足型4类。最后,提出广州市应以城市轨道交通廊道为整体来策划沿线车站的功能定位、周边用地开发强度和配套设施,从而推动形成城市轨道交通廊道上的职住梯度平衡。

Palm Print Identification Using Improved Histogram of Oriented Lines

Automatic palmprint identification has received much attention in security applications and law enforcement. The performance of a palmprint identification system is improved by means of feature extraction and classification. Feature extraction methods such as Subspace learning are highly sensitive to the rotation variances, translation and illumination in image identification. Thus, Histogram of Oriented Lines (HOL) has not obtained promising performance for palmprint recognition so far. In this paper, we propose a new descriptor of palmprint named Improved Histogram of Oriented Lines (IHOL), which is an alternative of HOL. Improved HOL is not very sensitive to changes of translation and illumination, and has the robustness against small transformations whereas the small translation and rotations make no change in histogram value adjustment of the proposed work. The experiment results show that based on IHOL, with Principal Component Analysis (PCA) subspace learning can achieve high recognition rates. The proposed method (IHOL-Cosine distance) improves 1.30% on PolyU I database, and similarly (IHOL-Euclidean distance) improves 2.36% on COEP database compared with existing HOL method.

一种近似BFGS的自适应双参数共轭梯度法

为了更加有效的求解大规模无约束优化问题,本文基于自调比无记忆BFGS拟牛顿法,提出一个自适应双参数共轭梯度法,设计的搜索方向满足充分下降性,在一般假设和标准Wolfe线搜索准则下,证明该方法具有全局收敛性,数值实验结果证明提出的新算法是有效的.

P波作用下土体孔隙尺寸及结构非均匀效应对圆形衬砌动力特性的影响

基于应变梯度非局部Biot理论,以深埋圆形衬砌为研究对象,利用波函数展开法和饱和土与衬砌间的边界条件,得到隧道衬砌在P波作用下的动力响应解析解。研究了不同入射P波频率下,非局部参数与尺寸因子对动应力集中系数(DSCF)的影响规律。结果表明,入射波频率较低时,非局部参数和尺寸因子对DSCF几乎没有影响,随着入射波频率的增大,非局部参数和尺寸因子对DSCF的影响会越来越明显,且非局部参数与DSCF呈负相关,尺寸因子与DSCF呈正相关;衬砌内动应力最大处均出现在衬砌右侧;随着频率的增加,衬砌内DSCF沿径向呈现明显的波动,非局部参数和尺寸因子对衬砌内环向应力的分布模式影响不大。

基于L0梯度平滑与图像分块聚类的海天线检测

海天线检测在海洋工程安防活动中具有重要的意义,真实海洋环境中的海天线检测易受云朵、海浪、光照变化、目标遮挡物、边界模糊等外界干扰。为了实现对真实海洋环境中海天线的检测,本研究提出一种基于L0梯度平滑和图像分块聚类的海天线检测算法。首先,对图像进行L0梯度平滑滤波,以增强海天线边缘,弱化非海天线因素干扰;接着,将图像沿着竖直方向分割成若干等宽图像块,以降低整体环境干扰,加强局部海天线检测效果;然后,通过Canny算子和霍夫变换提取每个分割图像块中的直线段;最后,采取K-means聚类算法提取每个图像块中的海天线段,拟合生成完整海天线。实验结果表明,在真实的海天线数据集中,本研究方法获取的矩形框重叠率平均精度为93.22%,角度差平均精度为7.66%,均高于文中选取的近年典型对比算法。满足实际海天线检测抗干扰强、准确率高、适应性广等要求。

基于借线遥控电极阵列的二维/三维电法勘探

借线遥控电极阵列是一种新型供电—观测电极阵列,它借助常规电法勘探的供电导线和测量导线载波传送信号,遥控各导线与其链接的系列编码电极开关,从而有序地开展供电和测量。这种阵列的电极点距可灵活改变,供电电极间距可逐渐遥控扩大,实现了梯度测深阵列化测量。借线遥控器可以与单道电测仪、多测道电法仪、高密度电法仪等配合使用,组合后电极的阵列能更有效地开展二维/三维电法勘探。应用实例表明,与传统探测方式或高密度方式相比较,借线遥控电极及其组合阵列在矿产、岩溶等复杂地形地质条件下展现出高效率和高灵活性,拓展了电法勘探深部探测应用技术体系,具有推广价值和应用前景。

一种WYL型谱共轭梯度法的全局收敛性

为解决大规模无约束优化问题,该文结合WYL共轭梯度法和谱共轭梯度法,给出了一种WYL型谱共轭梯度法.在不依赖于任何线搜索的条件下,该方法产生的搜索方向均满足充分下降性,且在强Wolfe线搜索下证明了该方法的全局收敛性.与WYL共轭梯度法的收敛性相比,WYL型谱共轭梯度法推广了线搜索中参数σ的取值范围.最后,相应的数值结果表明了该方法是有效的.