极大熵函数的梯度收敛性

本文讨论了极大炕函数的梯度收敛性

一个三项共轭梯度算法及其收敛性

本文给出一个三项共轭梯度算法,搜索方向在不需要任何线搜索的条件下,拥有充分下降性条件,在此方向的定义中,不但拥有梯度值信息还拥有函数值信息,证明了全局收敛性并给出数值检验结果。

基于有限元超收敛的三维节点型有限元后处理技术

在电磁法节点有限元正演模拟中,需要对主场的有限元解进行数值微分求取辅助场,或者求解位的有限元解,从而得到电磁场分量。针对传统的后处理方法精度较低的问题,引入一种超收敛单元片梯度值恢复(SPR)技术,应用于可控源电磁法节点有限元正演的后处理。首先,基于可控源电磁法的电场二次场双旋度方程,采用结构化的六面体网格和节点伽辽金有限元法求解电场(主场)分量;然后,根据节点有限元法的超收敛性质,以围绕某一节点的所有的单元组成单元片,在单元片上以高斯点作为采样点对电场梯度值进行最小二乘曲面拟合,恢复单元片上节点的电场梯度值;最后,计算高精度磁场,进而获得高精度的视电阻率和相位响应。模型算例分析表明,与常规的单元形函数微分(SFD)法、拉格朗日插值(LI)法和移动最小二乘(MLSI)法相比,超收敛单元片梯度值恢复后处理技术能在极小幅度地增加内存和计算时间的情况下,非常显著地提高磁场分量的精度并且保持良好的稳定性。

基于v-Informer的云平台资源负载预测方法

目前,云计算技术的使用非常广泛。随着用户量的增加,云计算资源的分配管理也越来越重要,而准确的负载预测是分配管理的重要依据。但由于云平台任务有多个负载特征,且特征的相关性变化趋势各不相同,因此难以从长期的历史数据中提取出有效的依赖信息。在Informer模型的基础上,提出了一种针对高动态云平台任务CPU长期负载预测方法v-Informer,该方法通过变分模态分解来分解负载序列中的变化趋势,引入多头自注意力机制捕获其中的长期依赖性和局部非线性关系,同时应用梯度集中技术改进优化器,减少计算开销。分别在微软云平台和谷歌云平台数据上进行实验,结果表明,与目前已有的CPU负载预测模型LSTM,Transformer,TCN和CEEMDAN-Informer相比,v-Informer在Google数据集上的预测误差分别减少了34%,19%,15%和6.5%;在微软数据集上的预测误差分别减少了32%,16%,12%和7%,具有较好的预测精度。

基于改进MobileNet的废钢识别方法研究

为了高效地判别废钢的种类,研究一种基于改进MobileNet的废钢识别方法,首先提出改进的MobileNetV3模型,并在此基础上通过通道剪枝方法去除冗余扩张通道,减少网络参数量,提升了模型预测速度。实验首先采集了4种不同废钢类型的数据集,并将数据集按80%为训练集,20%为验证集进行训练,然后和ResNet152模型、传统的MobileNetV3模型比较了模型的训练和损失曲线。训练结果表明,改进后的MobileNetV3模型在废钢类型识别任务上表现出色,其总体分类准确率达到了98%,优于ResNet152模型的97%和传统MobileNetV3模型的87%。这一结果充分证明了改进模型的有效性且该模型能在不同学习率下快速收敛梯度,可以高效地识别废钢。

一种改进的遗传卡尔曼算法在室内定位中的研究

提出了一种基于改进卡尔曼滤波和遗传算法的室内定位方法。首先利用共轭梯度收敛法计算稳态卡尔曼滤波器的增益值和离散时间卡尔曼滤波器的Riccati方程的解,该算法利用逼近自回归模型建立一步预测方程,所有非线性方程都可化为该线性方程求解。新方法利用卡尔曼滤波预测目标在下一时刻可能出现的位置,以该位置为中心建立该点的邻域,以预测目标坐标范围为模板,并且基于欧氏距离公式原则建立适应度函数,候选区的中心坐标为参数编码,结合遗传算法进行定位,对适应度函数通过泰勒级数展开式进一步优化定位坐标。实验结果表明,这种方法稳定性好,收敛速度快,有效消除噪声干扰,得到比较准确的位置坐标。

基于运动粒子的粒子群目标跟踪算法

为兼顾目标跟踪的准确度和目标跟踪时图像的处理速度,文章提出一种基于运动粒子的粒子群目标跟踪算法。该算法首先对目标跟踪区域提取HSV特征得到目标特征向量;然后以高斯分布的形式撒下n个粒子构成粒子群,通过梯度收敛算法可以快速准确地搜索到最佳的目标位置,并以此位置作为跟踪点,进行下一帧跟踪。实验结果表明,在精确度方面文章提出的算法是CSK算法的1.52倍、MS算法的1.57倍,在速度方面文章提出的算法是Struck算法的22.87倍、KCF算法的1.11倍,有效地兼顾了目标跟踪的准确度和处理速度。

一种有效的广义特征值分析方法

提出了一种适合于自适应有限元分析中求解广义特征值问题的多重网格方法 .这种方法充分利用了初始网格下的结果 ,通过插值或最小二乘拟合技术来得到网格变化后的新的近似特征向量 ,然后由多重网格迭代过程实现对结构广义特征值问题的求解 .在多重网格迭代的光滑步中 ,选择了收敛梯度法以提高其收敛率 ;在粗网格校正步中 ,则导出了一种近似求解特征向量误差的方程 .这种方法将网格离散过程和数值求解过程很好地相结合 ,建立了一个网格细分后广义特征值问题的快速重分析方法 ,与传统有限元方法相比较 ,具有计算简便、计算量少等特点 ,可以作为结构动力问题自适应有限元分析的一种十分有效的工具 .

Three-Dimensional Finite Element Superconvergent Gradient Recovery on Par6 Patterns

In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.

Full waveform inversion based on improved MLQN method

Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to study optimization method. The study is based on conventional Memoryless quasi-Newton( MLQN)method. Because the Conjugate Gradient method has ultra linear convergence,the authors propose a method by using Fletcher-Reeves( FR) conjugate gradient information to improve the search direction of the conventional MLQN method. The improved MLQN method not only includes the gradient information and model information,but also contains conjugate gradient information. And it does not increase the amount of calculation during every iterative process. Numerical experiment shows that compared with conventional MLQN method,the improved MLQN method can guarantee the computational efficiency and improve the inversion precision.

Full waveform inversion with spectral conjugategradient method

Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.

Modified Levenberg-Marquardt algorithm for source localization using AOAs in the presence of sensor location errors

In this paper,by utilizing the angle of arrivals(AOAs) and imprecise positions of the sensors,a novel modified Levenberg-Marquardt algorithm to solve the source localization problem is proposed.Conventional source localization algorithms,like Gauss-Newton algorithm and Conjugate gradient algorithm are subjected to the problems of local minima and good initial guess.This paper presents a new optimization technique to find the descent directions to avoid divergence,and a trust region method is introduced to accelerate the convergence rate.Compared with conventional methods,the new algorithm offers increased stability and is more robust,allowing for stronger non-linearity and wider convergence field to be identified.Simulation results demonstrate that the proposed algorithm improves the typical methods in both speed and robustness,and is able to avoid local minima.

Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.

Compression and reconstruction of speech signals based on compressed sensing

Based on the approximate sparseness of speech in wavelet basis,a compressed sensing theory is applied to compress and reconstruct speech signals.Compared with one-dimensional orthogonal wavelet transform(OWT),two-dimensional OWT combined with Dmeyer and biorthogonal wavelet is firstly proposed to raise running efficiency in speech frame processing,furthermore,the threshold is set to improve the sparseness.Then an adaptive subgradient projection method(ASPM)is adopted for speech reconstruction in compressed sensing.Meanwhile,mechanism which adaptively adjusts inflation parameter in different iterations has been designed for fast convergence.Theoretical analysis and simulation results conclude that this algorithm has fast convergence,and lower reconstruction error,and also exhibits higher robustness in different noise intensities.

A New Two-Parameter Family of Nonlinear Conjugate Gradient Method Without Line Search for Unconstrained Optimization Problem

This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.

基于改进的Inception-ResNet-V2废钢类型识别算法

本研究提出了一种基于深度学习的废钢快速识别方法,提出的基于Inception-ResNet-V2的改进网络结构添加注意力机制模块经过微调得到SE-Inception-ResNet,并在此基础上采用学习率梯度更新策略自适应调节优化模型。采集了四种类型的废钢数据,然后将样本图像按80%训练集,20%验证集进行训练。后与ResNet152、InceptionV3比较了模型的性能。结果表明,SE-Inception-ResNet、InceptionV3和ResNet152网络的总体分类准确率分别为98.10%、97.48%、95.67%。SE-Inception-ResNet的分类精度最高,该模型在不同学习率情况下能快速梯度收敛。实验结果表明,所提出的改进卷积神经网络模型能够有效地对废钢类型进行识别。同时期望提高其迁移学习模型泛化性,可以为其他快速分类鉴定提供参考,并应用于其他工业或商业领域。

Convergence of On-Line Gradient Methods for Two-Layer Feedforward Neural Networks

A discussion is given on the convergence of the on-line gradient methods for two-layer feedforward neural networks in general cases. The theories are applied to some usual activation functions and energy functions.

CONVERGENCE PROPERTIES OF THE DEPENDENT PRP CONJUGATE GRADIENT METHODS

In this paper, a new region of βk with respect to ;βk^PRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi （1997） and Dai and Yuan （2002）.

A NONMONOTONE CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.

Convergence analysis of projected gradient descent for Schatten-p nonconvex matrix recovery

The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) problem.Based on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.