求解鲁棒主成分分析的新交替下降方向法

鲁棒主成分分析作为统计与数据科学领域的基本工具已被广泛研究,其核心原理是把观测数据分解成低秩部分和稀疏部分.本文基于鲁棒主成分分析的非凸模型,提出了一种新的基于梯度方法和非单调搜索技术的高斯型交替下降方向法.在新算法中,交替更新低秩部分和稀疏部分相关的变量,其中低秩部分的变量是利用一步带有精确步长的梯度下降法进行更新,稀疏部分的变量是采用非单调搜索技术进行更新.本文在一定的条件下建立了新算法的全局收敛理论.最后的数值试验结果表明了新算法的有效性.

一种改进的求解单调变分不等式的平行分裂算法

为了求解一类可分结构的单调变分不等式,本文使用了一种改进的平行分裂算法,并给出了新算法的一个下降方向和沿着这个下降方向的最优步长,在合理的假设下,算法的收敛性得到了证明,一些数值试验表明新算法是有效的.

基于多层可行方向法液体静压转台优化设计

为提高液体静压转台的动力学性能,该文从N-S方程着手,计算了液体静压油腔处的动压承载力。通过供油压力计算了同位置处的静压承载力,利用动压承载力和静压承载力的相互叠加,计算了液体静压导轨综合承载力,继而推导了油膜刚度的计算公式。在此基础上,建立了以综合承载力和油膜刚度为目标函数,以液体静压转台的振动基频为约束的优化模型,利用响应面方法和分层可行下降方向法对优化模型进行了求解,并对优化后的设计进行了瞬态冲击载荷下加工精度的验证,从而为工程设计提供了理论依据。

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.

BFGS Method for Linear Programming

In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction and its fast convergence towards an optimal solution. Our proposed method is compared with Newton＇s method for linear program named lpnew, widely used as an optimization algorithm for classification problems.