An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

The Convergence of the Steepest Descent Algorithm for D.C.Optimization

伪可辨的函数(二个有限凸的函数的差别) 的一个类的一些性质在这份报纸被考虑。并且为非强迫、抑制的伪可辨的编程的最陡峭的降下算法的集中被证明。

Thrust Optimization of Flapping Wing via Gradient Descent Technologies

The current work aims at employing a gradient descent algorithm for optimizing the thrust of a flapping wing. An in-house solver has been employed, along with mesh movement methodologies to capture the dynamics of flow around the airfoil. An efficient framework for implementing the coupled solver and optimization in a multicore environment has been implemented for the generation of optimized solutionsmaximizing thrust performance & computational speed.

A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.

Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method

We introduce the fractional-order global optimal backpropagation machine,which is trained by an improved fractionalorder steepest descent method(FSDM).This is a fractional-order backpropagation neural network(FBPNN),a state-of-the-art fractional-order branch of the family of backpropagation neural networks(BPNNs),different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method.The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error.First,the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically.Then,the mathematical proof of fractional-order global optimal convergence,an assumption of the structure,and fractional-order multi-scale global optimization of the FBPNN are analyzed in detail.Finally,we perform three(types of)experiments to compare the performances of an FBPNN and a classic first-order BPNN,i.e.,example function approximation,fractional-order multi-scale global optimization,and comparison of global search and error fitting abilities with real data.The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.

CONVERGENCE ANALYSIS OF A LOCALLY ACCELERATED PRECONDITIONED STEEPEST DESCENT METHOD FOR HERMITIAN-DEFINITE GENERALIZED EIGENVALUE PROBLEMS

By extending the classical analysis techniques due to Samokish, Faddeev and Faddee- va, and Longsine and McCormick among others, we prove the convergence of the precon- ditioned steepest descent with implicit deflation （PSD-id） method for solving Hermitian- definite generalized eigenvalue problems. Furthermore, we derive a nonasymptotie estimate of the rate of convergence of the PSD-id method. We show that with a proper choice of the shift, the indefinite shift-and-invert preconditioner is a locally accelerated preconditioner, and is asymptotically optimal which leads to superlinear convergence Numerical examples are presented to verify the theoretical results on the convergence behavior of the PSD- id method for solving ill-conditioned Hermitian-definite generalized eigenvalue problems arising from electronic structure calculations. While rigorous and full-scale convergence proofs of preconditioned block steepest descent methods in practical use still largely eludes us, we believe the theoretical results presented in this paper shed light on an improved understanding of the convergence behavior of these block methods.

A multipath mitigation algorithm for GNSS signals based on the steepest descent approach

Multipath interference seriously degrades the performance of Global Navigation Satellite System(GNSS)positioning in an urban canyon.Most current multipath mitigation algorithms suffer from heavy computational load or need external assistance.We propose a multipath mitigation algorithm based on the steepest descent approach,which has the merits of less computational load and no need for external aid.A new ranging code tracking loop is designed based on the steepest descent method,which can save an early branch or a late branch compared with the narrow-spacing correlation method.The power of the Non-Line-of-Sight(NLOS)signal is weaker than that of the Line-of-Sight(LOS)signal when the LOS signal is not obstructed and with a relatively high Carrier Noise Ratio(CNR).The peak position in the X-axis of the ranging code autocorrelation function does not move with the NLOS interference.Meanwhile,the cost function is designed according to this phenomenon.The results demonstrate that the proposed algorithm outperforms the narrow-spacing correlation and the Multipath Estimated Delay Locked Loop(MEDLL)in terms of the code multipath mitigation and computation time.The Standard Deviation(STD)of the tracking error with the proposed algorithm is less than 0.016 chips.Moreover,the computation time of the proposed algorithm in a software defined receiver is shortened by 24.21%compared with the narrow-spacing correlation.

Three-step relaxed hybrid steepest-descent methods for variational inequalities

The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.

基于变增益最速梯度下降法的表贴式永磁同步电机位置修正策略

滑模观测器具有响应速度快、鲁棒性强等优点,已广泛应用于表贴式永磁同步电机无位置传感器的中、高速控制系统。然而,具有固定参数的滑模观测器很难在宽速度范围内保持一致的估算精度,而采用基于速度观测器带宽限制的方法进行噪声和扰动抑制会降低电机的动态性能。针对上述问题,该文首先分析滑模观测器估算表贴式永磁同步电机转子位置的误差产生机理,提出一种新型位置误差观测器,主要思想是基于磁链观测进行位置误差连续估算,并采用最速梯度下降法对积分过程进行反馈校正;然后,通过变增益循环迭代优化提高位置误差观测器的速度与准确性;最后搭建表贴式永磁同步电机加载测试平台进行实验,结果验证了所提方法具有位置观测精度高、鲁棒性强的特点。

双三相永磁同步电机鲁棒滑模预测速度控制

为提高双三相永磁同步电机系统应对复杂扰动时的鲁棒性,提出了一种带有最速下降观测器的滑模预测速度控制策略。通过将参数变化和外部扰动注入到q轴电流系数,建立了带有扰动的双三相永磁同步电机运动模型。基于电机扰动模型提出了一种滑模预测速度控制策略,该方案使用基于双曲正切函数的新型幂次趋近律,能够在保持较快跟踪速度的同时有效抑制滑模抖振。设计了一个基于最速下降算法的扰动观测器,用于估计随叠加扰动而时刻变化的q轴电流系数并将其传递到滑模预测速度控制模型中。与传统的滑模预测速度控制相比,仿真结果证明了所提方法具有较好的动态跟踪性能和扰动抑制性能。

关于Chidume-Zegeye-Ntatin定理的注释

带误差的Mann迭代及Ishikawa迭代一直众多学者关心的一个热点问题。本文中我们对Chidume-Zegeye-Ntatin定理进行探讨,具体工作如下:首先是定理中序列有界性的证明进行了改进;其次用更为简单的方法证明了该定理;最后所得结果推广和改进了相关的结论。

基于μPMU测量数据的配电网线路阻抗参数估计

为解决长期以来低压配电网线路阻抗参数缺失的问题,基于微型同步相量测量单元(micro phasor measurement unit,μPMU)提供的测量数据,首先,以线路阻抗参数为变量,根据测量数据推算台区首端状态值,以推算值与实测值的差值作为目标函数,将阻抗参数的求解转化为多目标最优化问题;然后,通过实验确定合适的目标函数权重系数取值和数据集大小,以减少误差对求解结果的影响,使模型求解精度达到较高水准;最后,搭建了包含26个负荷节点、34条线路支路的低压配电网台区算例,在考虑实际测量误差的情况下,线路阻抗参数计算平均误差为3.87%。算例结果表明,所提方法实现了阻抗参数的精确计算,验证了所提模型的有效性。

聚焦Kundu-Eckhaus方程的反散射变换法:阶跃振荡背景下的长时间渐进性

该文利用非线性速降法研究了阶跃振荡背景下聚焦Kundu-Eckhaus方程解的长时间渐进性问题.在稀疏情况下,当解趋于x轴时,其渐进性以平面波的形式呈现;当解趋于t轴时,其渐进性以缓慢衰减的形式呈现;而在两个过渡扇区,解的渐进性可表示为调制椭圆波函数.此外,在激波情况下,解的渐进性可由依赖于亏格为3的黎曼曲面的超椭圆函数表示.该文所得结论有助于解释存在五次非线性项以及自频移效应的调制不稳定性下的非线性阶段.

基于改进Richardson的大规模MIMO信号检测算法

在大规模多输入多输出(multiple-input multiple-output,MIMO)系统信号检测中,最小均方误差(minimum mean square error,MMSE)算法可以得到近似最优检测性能,然而该算法需要高维矩阵求逆,其复杂度很高,无法保证信号的实时检测。因此提出一种改进Richardson信号检测方法,利用最速下降法和整体修正法改进Richardson算法性能,最速下降法可以提供更有效地搜索路径,得到不同近似解,并且为了提高求解精度,利用整体修正法对不同近似解进行修正,使算法收敛速度更快,同时将算法复杂度数量级由O(K^(3))降低到O(K^(2))。仿真结果表明,该算法只需3次迭代就可接近MMSE,在降低复杂度的同时提高了误码率性能。

核电子学与核仪器中多步ADC的测试和校准

针对核电子学与核仪器中的多步模拟-数字变换器的测试和校准进行了研究。提出了基于工艺变化监测的校准思想和对于每一级的主要静态误差源即系统判决级偏移误差、级增益误差和内部参考电压误差的双残差信号处理方案。针对多级电路的校准提出了一种基于最速下降法的校准算法,通过比较估计输出和期望响应实现估计误差的创建。并针对基于模具级工艺监测器和温度传感器的工艺变化监测提出了两种估计算法,从而实现整个多步ADC的全量程测试和校准。

最速下降法的一次迭代收敛性的一点注记

推广了最速下降法经过一次迭代到达严格凸二次规划问题的最优解的充分必要条件:初始点可以表示为最优解和Hesse矩阵的一个特征向量之和.证明此条件也是最速下降法经过有限次迭代后到达最优解的充要条件.丰富了最速下降法的理论,有助于更好地认识和理解最速下降法,对相关算法的教学有一定的启发意义.

特征值与梯度下降算法

文中以特征值为工具,讨论了求解无约束优化问题的梯度下降法的步长和收敛速度的一些性质,并利用特征值解释了数据的标准化为何能提高最小二乘线性回归的收敛速度.

基于最速下降法的自适应环流抑制

针对交直流混合微电网孤岛运行时,并联变流器硬件参数不能完全一致,控制信号无法完全同步以及负荷波动导致并联回路中存在多种循环电流问题,提出一种基于最速下降法(SDM)的虚拟同步发电机(VSG)控制策略。通过最速下降法迭代得到循环电流最小时的变流器输出电压并反馈给VSG控制器,既实现各工况下VSG输出电压的同步,又有效地完成了负荷波动时的电压自适应调整。为了验证所提控制策略的有效性,在MATLAB/Simulink中搭建仿真模型,仿真结果表明所提控制方法可有效抑制系统环流。

改进的高阶收敛FastICA算法

高阶收敛的FastICA具有形式简单、收敛速度快的特点,但其对初始值的选择比较敏感,若初始值选择不当很容易影响收敛的效果,甚至造成不收敛的结果.针对这一问题,采用最速下降法对三阶和五阶收敛的FastICA算法进行改进.首先,应用最速下降法求出初值,再用高阶收敛的FastICA算法求出最优解.语音信号的分离实验表明:改进后的算法对混合信号进行了较好的分离,并且有效地克服了初值敏感性的问题.