A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

一个松弛非单调线搜索法

对于无约束优化问题,我们用松弛技术改进了一般非单调线搜索准则,建立了相应的求解算法,并证明了算法的整体收敛性.部分数值实验结果表明,这个松弛非单调算法有效.     

无约束最优化问题的BFGS并行算法与实现

介绍无约束最优化问题的BFGS算法及其收敛性,提出利用行卷帘格式并行Cholesky分解法、同步并行Wolfe-Powell非线性搜索和并行处理BFGS修正公式来构建BFGS的并行算法,并对该算法的时间复杂性、加速比进行分析。在PC机群数值实验的结果表明,BFGS并行算法提高了无约束最优化问题的求解速度,理论分析与实验结果相一致,并行算法具有线性加速比。     

The optimal retrieval of ocean color constituent concentrations based on the variational method

In this paper, a new approach to the optimal retrieval of the ocean color based on the variational method is developed by setting up a rational target functional combining with the Broydor Fletcher, Goldfarb, Shanno (BFGS) optimal algorithm. The numerical tests and the exemplary retrievals are carried out and compared with the statistical retrievals and the optimal retrievals based on the genetic algorithm. The results show that this approach enjoys a higher accuracy as compared to the statistical method and a higher efficiency as compared to the genetic algorithm. The optimal retrieval method presented in this paper provides a new idea for the ocean color inversion and could also be used as a reference for the direct assimilation of the satellite data into the ecological models.     

一种新型两相流检测ERT图像重建算法

针对目前电阻层析成像(ERT)应用于两相流领域重建图像算法存在成像精度较低和速度较慢的问题,基于BFGS最优化方法,提出一种新型图像重建算法.为满足两相流在线参数测量的要求,对BFGS算法进行了改进.改进的BFGS算法(MBFGS)选取了不精确的迭代方向,并用单位矩阵近似代替目标函数的Hessian矩阵.数值实验证明,新算法较为稳定和快速,重建图像的质量优于目前常用的灵敏度系数法和线性反投影算法,算法以较小的速度代价重建较高质量的图像.     

多波长辐射反问题重建燃烧一维温度分布

为了获得炉膛燃烧一维温度场,首先建立以二氧化碳和水蒸气为主的燃烧介质内一维辐射能传递模型,进而依据该模型,并结合二氧化碳和水蒸气的辐射特性参数的计算式,建立由边界处的辐射强度反演沿途火焰和介质一维温度分布的多波长辐射反问题.数值实验中利用BFGS算法求解此反问题获得燃烧的一维温度分布.数值实验的误差结果表明,此方法获得的重建一维温度分布整体及各段落温度值的相对误差均在10％以内,反演效果良好,能满足工业上的精度要求.     

基于混沌优化和BFGS方法的最优潮流算法

将混沌优化与拟牛顿法中的BFGS方法相结合，提出了一种新的混合优化算法，并应用该方法进行电力系统最优潮流的计算。混沌优化方法利用混沌运动内在的遍历性、随机性和规律性等特点，跳出局部最优解，接 近最优点；同时，利用BFGS方法在最优点的邻域内局部寻优，提高了收敛速度和求解精度。 通过对IEEE 14，30和57节点试验电力系统的数值计算，验证了算法的有效性。     

前馈神经网络的一种新的学习算法

本文将变尺度法引入到神经网络的学习中。在修改权值时，引入串行修正权值的思想。基于以上两点提出的算法具有收敛速度快、实习精度高等特点。     

A multiscale flaw detection algorithm based on XFEM

We present a novel multiscale algorithm for nondestructive detection of multiple flaws in structures, within an inverse problem type setting. The key idea is to apply a two‐step optimization scheme, where first rough flaw locations are quickly determined, and then, fine tuning is applied in these localized subdomains to obtain global convergence to the true flaws. The two‐step framework combines the strengths of heuristic and gradient‐based optimization methods. The first phase employs a discrete‐type optimization in which the optimizer is limited to specific flaw locations and shapes, thus converting a continuous optimization problem in the entire domain into a coarse discrete optimization problem with limited number of choices. To this end, we develop a special algorithm called discrete artificial bee colony. The second phase employs a gradient‐based optimization of the Broyden–Fletcher–Goldfarb–Shanno type on local well‐defined and bounded subdomains determined in the previous phase. A semi‐analytical approach is developed to compute the stiffness derivative associated with the evaluation of objective function gradients. The eXtended FEM (XFEM), with both circular and elliptical void enrichment functions, is used to solve the forward problem and alleviate the costly remeshing of every candidate flaw, in both optimization steps. The multiscale algorithm is tested on several benchmark examples to identify various numbers and types of flaws with arbitrary shapes and sizes (e.g., cracks, voids, and their combination), without knowing the number of flaws beforehand. We study the size effect of the pseudo grids in the first optimization step and consider the effect of modeling error and measurement noise. The results are compared with the previous work that employed a single continuous optimization scheme (XFEM–genetic algorithm and XFEM–artificial bee colony methods). We illustrate that the proposed methodology is robust, yields accurate flaw detection results, and in particular leads to significant improvements in convergence rates compared with the previous work. Copyright © 2014 John Wiley & Sons, Ltd.     

基于BFGS拟牛顿算法的含噪数字字符识别

针对传统数字字符识别算法收敛速度慢且有可能陷入局部极小值等问题,提出了将BFGS拟牛顿算法应用于含噪数字字符识别:构造前馈型神经网络,调用Matlab神经网络工具箱中的训练函数trainbfg对网络进行训练.该算法收敛速度快、识别精度高,能够对含有一定噪声的数字字符进行识别,具有广阔的应用前景.