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.

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.

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.

Local convergence zones or discontinuous lines in the Taklimakan Desert, Northwest China

In order to study convergence zones or discontinuous lines formed locally in the Taklimakan Desert,we analyzed available MODIS images onboad TERRA or AQUA satellite for ten cases:29 March 2002,14 April 2002;2 January 2003;21 April 2003;26 March 2004;28 April 2004;30 January 2005;25 June 2005;3 December 2005;and 26 July 2006.We used weather maps published by the Japan Mete-orological Agency for the Asia and Pacific region at 500 hPa,700 hPa and 850 hPa,at 00Z and 12Z to analyze the meteorological conditions occurring in each case.We estimated the positions of air streams,convergence zones or discontinuous lines between them,and thermal conditions on the maps and con-firmed the presence of cumulus and cumulonimbus clouds through satellite images in particular.After a review of previous studies,this paper introduced the results of the present study.Closed warm areas in the Taklimakan Desert and on the Tibetan Plateau and local convergence zones or discontinuous lines in the Taklimakan Desert were discussed together with their diurnal changes,using composite maps of the ten cases.Along the long axis of the desert the convergence zones or discontinuous lines normally extend 70-80 km in a west-east direction,but are suspected to exceed 100 km in extreme cases.On the other hand,the convergence zones or discontinuous lines extending in a north-south direction on the southern fringe of the desert have a length of 40-60 km.The closed warm areas show clear diurnal changes,but they were not detected at the 500 hPa level.An example of a clear convergence zone running in a north-south direction on 26 July 2006 was presented in detail with corresponding satellite images.

Global Convergence of an Extended Descent Algorithm without Line Search for Unconstrained Optimization

In this paper, we extend a descent algorithm without line search for solving unconstrained optimization problems. Under mild conditions, its global convergence is established. Further, we generalize the search direction to more general form, and also obtain the global convergence of corresponding algorithm. The numerical results illustrate that the new algorithm is effective.

The global convergence of the non-quasi-Newton methods with non-monotone line search

The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved. Numerical experiments showed that the non-monotone line search was more effective.

Several New Line Search Methods and Their Convergence

In this paper, we propose several new line search rules for solving unconstrained minimization problems. These new line search rules can extend the accepted scope of step sizes to a wider extent than the corresponding original ones and give an adequate initial step size at each iteration. It is proved that the resulting line search algorithms have global convergence under some mild conditions. It is also proved that the search direction plays an important role in line search methods and that the step size approaches mainly guarantee global convergence in general cases. The convergence rate of these methods is also investigated. Some numerical results show that these new line search algorithms are effective in practical computation.

Convective Initiation by Topographically Induced Convergence Forcing over the Dabie Mountains on 24 June 2010

The initiation of convective cells in the late morning of 24 June 2010 along the eastward extending ridge of the Dabie Mountains in the Anhui region, China, is studied through numerical simulations that include local data assimilation. A primary convergence line is found over the ridge of the Dabie Mountains, and along the ridge line several locally enhanced convergence centers preferentially initiate convection. Three processes responsible for creating the overall convergence pattern are identified. First, thermally-driven upslope winds induce convergence zones over the main mountain peaks along the ridge, which are shifted slightly downwind in location by the moderate low-level easterly flow found on the north side of a Mei-yu front. Second, flows around the main mountain peaks along the ridge create further convergence on the lee side of the peaks. Third, upslope winds develop along the roughly north-south oriented valleys on both sides of the ridge due to thermal and dynamic channeling effects, and create additional convergence between the peaks along the ridge. The superposition of the above convergence features creates the primary convergence line along the ridge line of the Dabie Mountains. Locally enhanced convergence centers on the primary line cause the initiation of the first convection cells along the ridge. These conclusions are supported by two sensitivity experiments in which the environmental wind （dynamic forcing） or radiative and land surface thermal forcing are removed, respectively. Overall, the thermal forcing effects are stronger than dynamic forcing given the relatively weak environmental flow.

Feasible SQP Descent Method for Inequality Constrained Optimization Problems and Its Convergence

In this paper,the new SQP feasible descent algorithm for nonlinear constrained optimization problems presented,and under weaker conditions of relative,we proofed the new method still possesses global convergence and its strong convergence.The numerical results illustrate that the new methods are valid.

Convergence Analysis on a Class of Nonmonotone Conjugate Gradient Methods without Sufficient Decrease Condition

In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.

Research on Narrowband Line Spectrum Noise Control Method Based on Nearest Neighbor Filter and BP Neural Network Feedback Mechanism

Thefilter-x least mean square(FxLMS)algorithm is widely used in active noise control(ANC)systems.However,because the algorithm is a feedback control algorithm based on the minimization of the error signal variance to update thefilter coefficients,it has a certain delay,usually has a slow convergence speed,and the system response time is long and easily affected by the learning rate leading to the lack of system stability,which often fails to achieve the desired control effect in practice.In this paper,we propose an active control algorithm with near-est-neighbor trap structure and neural network feedback mechanism to reduce the coefficient update time of the FxLMS algorithm and use the neural network feedback mechanism to realize the parameter update,which is called NNR-BPFxLMS algorithm.In the paper,the schematic diagram of the feedback control is given,and the performance of the algorithm is analyzed.Under various noise conditions,it is shown by simulation and experiment that the NNR-BPFxLMS algorithm has the following three advantages:in terms of performance,it has higher noise reduction under the same number of sampling points,i.e.,it has faster convergence speed,and by computer simulation and sound pipe experiment,for simple ideal line spectrum noise,compared with the convergence speed of NNR-BPFxLMS is improved by more than 95%compared with FxLMS algorithm,and the convergence speed of real noise is also improved by more than 70%.In terms of stability,NNR-BPFxLMS is insensitive to step size changes.In terms of tracking performance,its algorithm responds quickly to sudden changes in the noise spectrum and can cope with the complex control requirements of sudden changes in the noise spectrum.

A Descent Gradient Method and Its Global Convergence

Y Liu and C Storey(1992)proposed the famous LS conjugate gradient method which has good numerical results.However,the LS method has very weak convergence under the Wolfe-type line search.In this paper,we give a new descent gradient method based on the LS method.It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search.Finally,we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP^+method.

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.

A MIXED SUPERLINEARLY CONVERGENT ALGORITHM WITH NONMONOTONE SEARCH FOR CONSTRAINED OPTIMIZATIONS

In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.

华北局地大暴雨过程中多个β中尺度对流系统发生发展对比分析

利用常规地面高空观测、多普勒雷达、风廓线、VDRAS(Variational Doppler Radar Analysis System)和NCEP再分析资料,对2018年8月5—6日副热带高压(以下简称副高)控制下华北一次局地大暴雨过程中多个β中尺度对流系统触发和发展机制进行了分析。结果表明:这次大暴雨发生在副高控制下,处于高温、高湿气团中,大气层结极不稳定。暴雨由多个相继发展的中尺度对流系统造成,分别是太行山迎风坡上西南—东北向、华北平原地区保定一带南北向、保定至霸州附近西南—东北向和以雄安新区为中心东西向原地生消的准静止MCS-Ⅰ、MCS-Ⅱ、MCS-Ⅲ和MCS-Ⅳ,均属于β中尺度。在相似的环境中,不同中尺度对流系统触发机制有较大差异,太行山迎风坡上的MCS-Ⅰ是由近地层偏东暖湿气流在迎风坡与山风形成的辐合抬升触发;由辐射差异和前期强降水形成的局地冷池受MCS-Ⅰ影响再次加强后,其出流与环境风形成的两条地面辐合线分别触发了MCS-Ⅱ和MCS-Ⅲ,并组织对流沿辐合线呈带状发展;而超低空偏东风增强叠加冷池出流在地形抬升作用下促使沿山暖湿气团进一步抬升,使得原本消亡的MCS-Ⅰ再次重建。MCS-Ⅳ发展最旺盛、持续时间最长,是大暴雨中心的直接制造者,一方面MCS-Ⅱ与MCS-Ⅲ、MCS-Ⅰ与MCS-Ⅳ的两次合并过程,是MCS-Ⅳ增强、持久的重要原因;另一方面边界层偏东风急流为MCS-Ⅳ的发展提供了水汽和不稳定能量等有利条件,同时推动其左前方中尺度涡旋的发展,导致MCS-Ⅳ所在地的气旋性涡度大大增加,加强了以急流轴为中心的垂直次级环流发展,造成MCS-Ⅳ的发展维持,形成华北平原地区以雄安新区为中心的东西向大暴雨带。

金沙江下游峡谷一次飑线和下击暴流的机理分析

产生极端灾害性大风的飑线对水电站安全至关重要。本文以2016年6月4日金沙江下游白鹤滩水电站峡谷产生13级大风的飑线为例,从天气系统和中小尺度上讨论其形成机制。获得以下结论:(1)飑线到达前,受飑前低压影响水电站气压稳降了9 hPa,气温上升超过14℃。飑线到达时受雷暴高压作用1 h内气压陡升10 hPa,气温骤降超过10℃,相对湿度陡增到70%,伴随短时降水发生。飑线过境后以上要素恢复到原值。(2)天气尺度环流的分析发现,飑线当天水电站在高空急流入口右侧辐散和低空西南涡南侧切变辐合的耦合作用下,次级环流的上升运动为飑线深对流提供了环境背景。飑线前中高层干冷平流叠加在中低层暖湿平流上,加上低空强烈升温增加了气温直减率,积累了对流发展的静力和对流不稳定,为飑线长生命提供了有利环境条件。垂直风速显示峡谷的上空下沉运动增强了动量下传,促进飑线前侧的抬升,正反馈作用下促进风暴稳定发展。(3)昭通雷达探测表明,飑线中30 dBZ以上多单体紧密聚合成带状回波,镶嵌着超过10 km高度柱状发展的50 dBZ以上强回波核。径向速度场上,垂直于峡谷的中尺度辐合线与带状强回波吻合,是飑线的触发机制,对应深厚的中层径向辐合MARC(Mid-Altitude Radial Convergence)特征。在云体剖面结构上,飑线前强上升运动形成穹窿,飑线到达时高悬的回波核快速下降,形成下击暴流,并诱发顺着河谷的新单体生成,改变了飑线走向,形成顺着的峡谷的极端大风。

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.

地面堆载下盾构隧道结构韧性演化规律研究

韧性理论的提出和发展为盾构隧道结构性能评估提供了新思路。在提出考虑历史最大变形的衬砌性能指标基础上,建立包含管片、接头和非线性土弹簧的精细化三维有限元分析模型,研究了地面堆卸载作用下,不同埋深盾构隧道结构响应特征和韧性演化规律。结果表明:地面堆载下拱顶、拱底内弧面受拉,拱腰外弧面受拉,受错缝拼装影响,结构内力和损伤集中于边环纵缝相邻的中环管片处;卸载阶段隧道水平收敛减小,完全卸载后的残余变形随堆载量增加而增大,相同水平收敛情况下浅埋隧道卸载后变形恢复率大;隧道结构韧性随着水平收敛的增大快速降低,而缩短响应时间、提高修复措施效率可以提升隧道结构韧性;将隧道结构韧性分为4个等级,当结构进入极低韧性阶段时,应采取更加高效快速的综合修复方案,同时避免造成结构的二次损伤。

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.