基于预条件共轭梯度法的混凝土层析成像

根据常规图像重建的共轭梯度迭代算法,提出一种预条件共轭梯度法。用一种新的预条件子M来改善系数矩阵的条件数,结合一般的共轭梯度法,导出预条件共轭梯度法。实验结果表明,预条件共轭梯度算法比共轭梯度算法具有更好的CT重建效果和消噪能力,可提高计算的精度和图像的重建质量。     

带共轭梯度算子的爆炸搜索算法

爆炸搜索算法作为一种全局优化算法,在迭代后期会出现收敛速度慢、精度低的问题,而传统的优化算法恰好能克服这些缺点。因此,引入一种传统算法——近似共轭梯度法,即用差商代替导数的共轭梯度法。在此基础上,提出了带共轭梯度算子的爆炸搜索算法,先引入了新的变异算子来提高算法的全局搜索能力,再运用共轭梯度法添加一个新的算子——共轭梯度算子,实现对最优炸点的局部搜索,从而提高算法的收敛速度与精度。6个常用的benchmark函数的测试结果说明,改进算法的优化结果明显优于原算法。     

求解多集分裂可行问题的一种共轭梯度法

基于求解多集分裂可行问题与非线性最优化问题的等价性,考虑Jinling Zhao and Qingzhi Yang在[1]中提出的求解SFP的共轭梯度法和Censor等在[2]中提出的梯度投影法,尝试运用共轭梯度法求解多集分裂可行问题;并且证明了所构造算法的收敛性．提出的新算法克NT求矩阵逆的缺点．初步的数值结果表明新算法对于不同的问题都能够有较快的收敛速度,具有良好的稳定性和可行性,在问题维数增大时表现得越发明显．     

大型复线性方程组预处理双共轭梯度法

当复线性方程组的规模较大或系数矩阵的条件数很大时,系数矩阵易呈现病态特性,双共轭梯度法存在不收敛和收敛速度慢的潜在问题,采用适当的预处理技术,可以改善矩阵病态特性,加快收敛速度。从实型不完全Cholesky分解预处理方法出发,构造了一种针对复线性方程组的预处理方法,结合双共轭梯度法,给出了一种预处理双共轭梯度法。数值算例表明该算法求解速度快,可靠高效,能够应用于大型复线性方程组的求解。     

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。     

基于改进混合粒子群算法的电力系统无功优化

引入局部搜索能力强的共轭梯度法对粒子群算法进行改进,在粒子群算法陷入停滞时,把当前最优解作为共轭梯度法的初始点,再用共轭梯度法做运算,使算法跳出局部最优,大大改善了粒子群算法的性能.将该混合算法用于求解 IEEE30节点系统无功优化问题,算例结果验证了该算法的有效性.     

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。     

利用混沌搜索全局最优的一种混合算法

把共轭梯度法与混沌优化方法相结合，提出了一种混合优化算法，该算法能使共轭梯度法跳出局部最优，最终获得全局最优，算法的收敛性也进行证明，仿真表明算法是有效的。     

嵌入共轭梯度法的混合蛙跳算法

针对基本蛙跳算法在处理复杂函数优化问题时求解精度低且易陷入局部最优的缺点,提出了一种嵌入共轭梯度法的混合蛙跳算法。该算法在基本蛙跳算法划分模因组的基础上引入共轭梯度法,由于基本蛙跳算法模因组的划分规则,使得排在最后的青蛙子群个体位置较差,严重影响着整个群体的寻优速度,因而选取排列在后面的一部分模因组使用共轭梯度法进行求解,这使得算法在进化中后期易跳出局部最优,提高了算法的收敛精度。所得混合蛙跳算法有效结合了基本蛙跳算法较强的全局搜索能力和共轭梯度法快速精确的局部搜索能力。数值实验结果表明,所提出的改进蛙跳算法较基本蛙跳算法具有更高的收敛精度,避免了陷入局部最优的缺点,且优化结果更加稳定。     

基于改进人工萤火虫算法的无线传感网络覆盖优化

为了提高网络资源利用率延长网络生存时间,提出一种基于共轭梯度法改进人工萤火虫算法(CAGSO)的WSN覆盖优化方案;共扼梯度法是利用目标函数的梯度逐步产生共轭方向并将其作为搜索方向的方法,即利用已知点处的梯度构造一组共扼方向并沿这组共扼方向进行搜索,这种方法经有限次迭代必达极小点;首先建立以覆盖率、节点利用率和能量均匀为准则的覆盖优化数学模型,然后采用改进的CAGSO算法求解该模型,从而得出最优覆盖方案;仿真分析说明,相比基本人工萤火虫算法,改进的CAGSO算法优化的网络覆盖率可以达到94.11%,有效实现WSN覆盖优化。     

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:     

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.     

A scaled conjugate gradient method for nonlinear unconstrained optimization

We propose a new optimization problem which combines the good features of the classical conjugate gradient method using some penalty parameter, and then, solve it to introduce a new scaled conjugate gradient method for solving unconstrained problems. The method reduces to the classical conjugate gradient algorithm under common assumptions, and inherits its good properties. We prove the global convergence of the method using suitable conditions. Numerical results show that the new method is efficient and robust.     

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.     

Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization

The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.     

Two modified spectral conjugate gradient methods and their global convergence for unconstrained optimization

In this paper, two modified spectral conjugate gradient methods which satisfy sufficient descent property are developed for unconstrained optimization problems. For uniformly convex problems, the first modified spectral type of conjugate gradient algorithm is proposed under the Wolfe line search rule. Moreover, the search direction of the modified spectral conjugate gradient method is sufficiently descent for uniformly convex functions. Furthermore, according to the Dai–Liao's conjugate condition, the second spectral type of conjugate gradient algorithm can generate some sufficient decent direction at each iteration for general functions. Therefore, the second method could be considered as a modification version of the Dai–Liao's algorithm. Under the suitable conditions, the proposed algorithms are globally convergent for uniformly convex functions and general functions. The numerical results show that the approaches presented in this paper are feasible and efficient.     

Comparing robust forms of iterative methods of conjugate directions

Simple and robust formulas of the conjugate direction method for symmetric matrices and of the symmetrized conjugate gradient method for nonsymmetric matrices have been constructed. These methods were compared with robust forms of the conjugate gradient method and the Craig method using test problems. It is shown that stability for the round-off error can be attained when recurrent variants of the methods are used. The most reliable and efficient method for symmetric signdefinite and indefinite matrices appears to be the method of conjugate residuals. For nonsymmetric matrices, the best results have been obtained by the method of symmetrized conjugate gradients. These two methods are recommended for writing standard programs. A reliable criterion has also been constructed for the termination of the calculation on reaching background values due to the round-off errors.     

模糊图像恢复的投影重开始共轭梯度法

针对点扩散函数为线性位移不变的图像恢复问题提出了一种重开始的投影共轭梯度法．该方法结合正则化技术,分两层迭代,采用阻尼Morozov偏差原则作为停机准则,在运算中利用快速傅立叶变换减少计算复杂度．并对二维遥感灰度图像和彩色图像分别进行数值实验,验证了该方法可以有效的再现原始图像,证明了算法的有效性．     

A self correcting conjugate gradient algorithm

In this paper we develop a new procedure for constructing a conjugate gradient direction equation. The new equation is a linear combination of two orthogonal vectors one of which is the negative gradient. This procedure is reduced to the method of Polak-Ribiere whenever line search is perfectly accurate. Otherwise, as reflected by our computational results, the method is more effective than any other conjugate gradient algorithm we have tested.