基于混合粒子群算法的烧结配料优化

在引入惩罚函数和对目标函数进行适当修改的前提下,充分利用粒子群优化算法的全局搜索能力和约束条件下共轭梯度法的局部搜索能力,设计了烧结配料优化算法．利用惩罚函数方法将约束条件优化问题转化为无约束条件优化问题,然后利用粒子群优化算法进行寻优．当群体最优信息陷入停滞时将目标函数进行适当变化,继续利用共轭梯度法进行寻优．计算结果表明,采用该方法能够在提高混合料中的有用成分、降低有害成分的前提下,更多地降低生产成本．     

修正PRP共轭梯度法的全局收敛性及其数值结果

本文提出了一种求解无约束优化问题的修正PRP共轭梯度法．算法采用一个新的公式计算参数,避免了产生较小的步长．在适当的条件下,证明了算法具有下降性质,并且在采用强Wolfe线搜索时,算法是全局收敛的．最后,给出了初步的数值试验结果．     

无约束优化的两类变参数共轭梯度法

§１．引言 共轭梯度法是求解无约束优化问题ｍｉｎ ｆ（ｘ）的一类非常重要且有效的方法．当目标函数ｆ（ｘ）连续可做时,其迭代格式为这里 ｑｋ＝ 　ｆ（ｘｋ）,ｄｋ是一个搜索方向．当 ｆ（ｋ）为凸二次函数时,适当选择系数 Ｂｋ－１,使得ｄｋ与ｄｌ,ｄ２,…,ｄｋ－１关于ｆ（ｘ）的Ｈｅｓｓｅ矩阵共轭。ａｋ是由精确线性搜索确定的步长．共轭梯度法具有二次终止性．然而当目标函数为一般的非线性函数时,即使在精确线性搜索下,各共轭梯度法的收敛性也很难保证．［１,２］证明了 ＦＲ方法在精确线性搜索下仍具有全局收敛性．然…     

一种改进的共轭梯度法及全局收敛性

在DY共轭梯度法的基础上对解决无约束最优化问题提出一种改进的共轭梯度法．该方法在标准wolfe线搜索下具有充分下降性，且算法全局收敛．数值结果表明了该算法的有效性．最后将算法用于SO2氧化反应动力学模型的非线性参数估计，获得满意效果．     

一种改进的无导数共轭梯度法

本文基于共轭梯度法的子空间研究,针对无约束优化问题提出了一种改进的无导数共轭梯度法。新算法不仅能有效弥补经典共轭梯度法要求线搜索为精确搜索的局限性,而且可适用于导数信息不易求得甚至完全不可得的问题。实验结果表明:相比于一次多项式插值法、有限差商共轭梯度法以及有限差商拟牛顿法,新算法的效率有很大的提高。     

一种克服粒子群早熟的混合优化算法

针对粒子群优化算法在寻优时容易出现早熟现象,提出在粒子群收敛停滞时,从种群中随机选择粒子进行共轭梯度法计算,通过引入共轭梯度算法计算的信息来影响粒子速度的更新,以保持群体的活性,从而打破群体信息陷入局部最优的状况.不同于传统的粒子群算法,该算法有机地结合了粒子群的全局搜索能力和共轭梯度法的强大局部搜索能力,从而在一定程度上有效地克服了粒子群早熟的缺点.仿真计算结果表明,该改进粒子群的方法对于不同维数的非线性函数具有很好的寻优效果.     

一种新型高效的计算机寻优算法

提出一种全新的寻找无约束最优解的计算机算法。该算法能使得目标函数梯度的模逐渐收缩到零,以达到目标函数极小化,因此命名“梯度收缩法”。它同时利用了牛顿法和共轭梯度法的优点,应用目标函数的二阶导数,收敛很快,且具有牛顿法的“二次终止”特性。但Hessian矩阵奇异时,牛顿法将无法进行下去,该文算法可以克服这个缺点且能快速确定是否收敛到一个鞍点。     

共轭梯度与牛顿混杂算法及在神经网络的应用

在Powell重启动共轭梯度法基础上,利用共轭迭代过程产生的二阶导数信息,构造出当前点的牛顿方向,从而得出一类快速共轭梯度法。用于神经网络逼近非线性函数的学习结果表明,该算法的收敛速度均高于使用相同构造公式的共轭梯度算法。     

基于梯度追踪的MIMO-OFDM稀疏信道估计算法

现有的压缩感知MIMO-OFDM信道估计方法多采用正交匹配追踪算法及其改进的算法。针对该类算法重构大规模的数据存在计算复杂度高、存储量大等问题,提出了基于梯度追踪算法的MIMO-OFDM 稀疏信道估计方法。梯度追踪算法采用最速下降法对目标函数解最优解,即每步迭代时计算目标函数的搜索方向和搜索步长,并以此选择原子得到每次迭代重构值的最优解。本文使用梯度追踪算法对信道进行估计,并与传统的最小二乘估计算法、正交匹配追踪算法的性能和计算复杂度进行比较。仿真结果表明,梯度追踪算法能够保证较好的估计效果,减少了导频开销,降低了运算复杂度,提高了重构效率。     

基于非线性共轭梯度法的混沌微粒群优化算法

为了寻找多峰函数的全部极值点,提出一种基于非线性共轭梯度法的混沌微粒群算法.该算法引入混沌序列设置微粒群位置以提高种群的多样性;然后使用改进的微粒群认知模型对可行域内的所有极值点进行全局搜索;最后利用非线性共轭梯度法对混沌微粒群算法搜索到的较优解进行局部搜索以提高解的精度.仿真实验表明,该算法能准确、快速地找到连续可微多峰函数的全部极值点.     

非线性预处理共轭斜量法

我们以Engli(1959)的线性方法为基础,构造出一个极小化一般非线性目标函数(3)的非线性预处理共轭斜量法:     

Convergence properties of a class of nonlinear conjugate gradient methods

Conjugate gradient methods are a class of important methods for unconstrained optimization problems, especially when the dimension is large. In this paper, we study a class of modified conjugate gradient methods based on the famous LS conjugate gradient method, which produces a sufficient descent direction at each iteration and converges globally provided that the line search satisfies the strong Wolfe condition. At the same time, a new specific nonlinear conjugate gradient method is constructed. Our numerical results show that the new method is very efficient for the given test problems by comparing with the famous LS method, PRP method and CG-DESCENT method.     

基于外时延反馈人工神经网络的短期负荷预测系统

针对当前人工神经网络学习算法存在的问题,使用变步伐最速下降法和共轭梯度法的混合算法来进行神经网络的训练,并建立了负荷预测的人工神经网络模型。介绍了基于Delphi下的短期电力负荷预测系统。该系统由负荷预测数据查询模块、预测方法模块、结果查询模块和图表输出模块四部分组成。事实说明,混合算法在全局收敛性和收敛速度上要好于传统的算法,所基于此的短期负荷预测系统能达到令人满意的精度。     

Sufficient descent conjugate gradient methods for large-scale optimization problems

Sufficient descent condition is very crucial in establishing the global convergence of nonlinear conjugate gradient method. In this paper, we modified two conjugate gradient methods such that both methods satisfy this property. Under suitable conditions, we prove the global convergence of the proposed methods. Numerical results show that the proposed methods are efficient for the given test problems.     

最速下降与共轭梯度在数字波束形成中的研究

在自适应波束形成技术中,共轭梯度法是求解最优化问题的一种常用方法,最速下降法在不需要矩阵求逆的情况下,通过递推方式寻求加权矢量的最佳值。文中将最速下降法与共轭梯度法有机结合,构造出一种混合的优化算法。该方法在每次更新迭代过程中,采用负梯度下降搜索方向,最优自适应步长,既提高了共轭梯度算法的收敛速度,又解决了最速下降法在随相关矩阵特征值分散程度增加而下降缓慢的问题,具有收敛速度快,运算量低的特点。计算机仿真给出了五阵元均匀线阵的数字波束形成系统实例,分别从波束形成、误差收敛及最佳权值等方面与传统LMS 算法进行了比较分析,结果表明了该方法的可行性与有效性。     

A sufficient descent conjugate gradient method and its global convergence

In this paper, a DL-type conjugate gradient method is presented. The given method is a modification of the Dai–Liao conjugate gradient method. It can also be considered as a modified LS conjugate gradient method. For general objective functions, the proposed method possesses the sufficient descent condition under the Wolfe line search and is globally convergent. Numerical comparisons show that the proposed algorithm slightly outperforms the PRP+ and CG-descent gradient algorithms as well as the Barzilai–Borwein gradient algorithm.     

Self-scaled conjugate gradient training algorithms

This article presents some efficient training algorithms, based on conjugate gradient optimization methods. In addition to the existing conjugate gradient training algorithms, we introduce Perry's conjugate gradient method as a training algorithm [A. Perry, A modified conjugate gradient algorithm, Operations Research 26 (1978) 26–43]. Perry's method has been proven to be a very efficient method in the context of unconstrained optimization, but it has never been used in MLP training. Furthermore, a new class of conjugate gradient (CG) methods is proposed, called self-scaled CG methods, which are derived from the principles of Hestenes–Stiefel, Fletcher–Reeves, Polak–Ribière and Perry's method. This class is based on the spectral scaling parameter introduced in [J. Barzilai, J.M. Borwein, Two point step size gradient methods, IMA Journal of Numerical Analysis 8 (1988) 141–148]. The spectral scaling parameter contains second order information without estimating the Hessian matrix. Furthermore, we incorporate to the CG training algorithms an efficient line search technique based on the Wolfe conditions and on safeguarded cubic interpolation [D.F. Shanno, K.H. Phua, Minimization of unconstrained multivariate functions, ACM Transactions on Mathematical Software 2 (1976) 87–94]. In addition, the initial learning rate parameter, fed to the line search technique, was automatically adapted at each iteration by a closed formula proposed in [D.F. Shanno, K.H. Phua, Minimization of unconstrained multivariate functions, ACM Transactions on Mathematical Software 2 (1976) 87–94; D.G. Sotiropoulos, A.E. Kostopoulos, T.N. Grapsa, A spectral version of Perry's conjugate gradient method for neural network training, in: D.T. Tsahalis (Ed.), Fourth GRACM Congress on Computational Mechanics, vol. 1, 2002, pp. 172–179]. Finally, an efficient restarting procedure was employed in order to further improve the effectiveness of the CG training algorithms. Experimental results show that, in general, the new class of methods can perform better with a much lower computational cost and better success performance.     

具有最小稳态误差的最优控制系统设计

稳态误差是控制系统设计中一项非常重要的性能指标，本文利用线性二次型（ＬＱ）最优控制系统设计中状态加权阵Ｑ的自由度，提出了一种具有最小稳态误差的ＬＱ最优控制系统设计方法。文中针对定义的稳态误差指标，推导其关于加权阵Q的梯度矩阵计算公式，从而将共轭梯度优化算法中非常有效的Beale算法和Armijo法则应用到设计方法中，给出了在计算机上易于实现的详细设计算法，通过实例仿真计算，验证了本设计方法的有效性，并获得了许多有意义的结果。     

Scaling techniques for gradient projection-type methods in astronomical image deblurring

The aim of this paper is to present a computational study on scaling techniques in gradient projection-type (GP-type) methods for deblurring of astronomical images corrupted by Poisson noise. In this case, the imaging problem is formulated as a non-negatively constrained minimization problem in which the objective function is the sum of a fit-to-data term, the Kullback–Leibler divergence, and a Tikhonov regularization term. The considered GP-type methods are formulated by a common iteration formula, where the scaling matrix and the step-length parameter characterize the different algorithms. Within this formulation, both first-order and Newton-like methods are analysed, with particular attention to those implementation features and behaviours relevant for the image restoration problem. The numerical experiments show that suited scaling strategies can enable the GP methods to quickly approximate accurate reconstructions and then are useful for designing effective image deblurring algorithms.