Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations

Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, I.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix.The igenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient,and the effect of image restoration is r0easonably well.

A branch-and-bound algorithm for multi-dimensional quadratic 0-1 knapsack problems

In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems.

Numerical Solutions for Quadratic Integro-Differential Equations of Fractional Orders

In this article, variational iteration method (VIM) and homotopy perturbation method (HPM) solve the nonlinear initial value problems of first-order fractional quadratic integro-differential equations (FQIDEs). We use the Caputo sense in this article to describe the fractional derivatives. The solutions of the problems are derived by infinite convergent series, and the results show that both methods are most convenient and effective.

ENERGY AND QUADRATIC INVARIANTS PRESERVING METHODS FOR HAMILTONIAN SYSTEMS WITH HOLONOMIC CONSTRAINTS

We introduce a new class of parametrized structure–preserving partitioned RungeKutta(α-PRK)methods for Hamiltonian systems with holonomic constraints.The methods are symplectic for any fixed scalar parameterα,and are reduced to the usual symplectic PRK methods like Shake-Rattle method or PRK schemes based on Lobatto IIIA-IIIB pairs whenα=0.We provide a new variational formulation for symplectic PRK schemes and use it to prove that theα-PRK methods can preserve the quadratic invariants for Hamiltonian systems subject to holonomic constraints.Meanwhile,for any given consistent initial values(p0,q0)and small step size h>0,it is proved that there existsα∗=α(h,p0,q0)such that the Hamiltonian energy can also be exactly preserved at each step.Based on this,we propose some energy and quadratic invariants preservingα-PRK methods.Theseα-PRK methods are shown to have the same convergence rate as the usual PRK methods and perform very well in various numerical experiments.

MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION

We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX^2 ＋ BX ＋ C = 0, where A, B and C are square matrices. This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices. Under suitable conditions, we prove the local linear convergence of the new method. An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm. In addition, we also describe and analyze the block version of the modified Bernoulli iteration method.

基于机器视觉的软磨片定位测量系统

针对软磨片外轮廓定位测量过程中,边缘较难提取,轮廓圆心与半径拟合精度较低的问题,提出通过中值滤波和灰度变换改善图像质量,使用灰度投影与灰度方差统计进行边缘筛选,利用圆心约束最小二乘法拟合外轮廓,通过高斯—牛顿法得到轮廓圆心坐标与半径,完成高精度定位和测量。通过实验对比,系统定位与测量误差保持在0.2mm以内,检测速度达到每片0.8s,在生产应用中具有实用性和高效性,提高了软磨片的检测效率和生产自动化程度。

抗间歇采样转发干扰的发射波形与失配滤波器联合优化算法

间歇采样转发干扰(interrupted sampling repeater jamming,ISRJ)与发射信号之间具有强相关性,若在接收端采用匹配滤波处理则会产生多个数量可控的高逼真假目标,对雷达的检测性能具有极大的干扰。针对上述问题,提出了一种抗ISRJ的发射波形和接收滤波器联合优化算法,将失配滤波体制下的信噪比(signal to noise ratio,SNR)损失、发射信号恒模约束以及滤波器能量约束考虑在内,以最小化干扰信号归一化脉压后峰值、失配滤波输出信号积分副主比以及输出干信比,并采用主分量最小化(majorization-minimization,MM)方法与平方迭代加速算法提高算法运行速度。仿真结果表明,与其他同类方法相比,所提算法能在保证可靠抗干扰性能的同时,极大缩短运行时间,具有较好的实时性。

Multi-loop Constrained Iterative Model Predictive Control Using ARX -PLS Decoupling Structure

A multi-loop constrained model predictive control scheme based on autoregressive exogenous-partial least squares(ARX-PLS) framework is proposed to tackle the high dimension, coupled and constraints problems in industry processes due to safety limitation, environmental regulations, consumer specifications and physical restriction. ARX-PLS decoupling character enables to turn the multivariable model predictive control(MPC) controller design in original space into the multi-loop single input single output(SISO) MPC controllers design in latent space.An idea of iterative method is applied to decouple the constraints latent variables in PLS framework and recursive least square is introduced to identify ARX-PLS model. This algorithm is applied to a non-square simulation system and a stirred reactor for ethylene polymerizations comparing with adaptive internal model control(IMC) method based on ARX-PLS framework. Its application has shown that this method outperforms adaptive IMC method based on ARX-PLS framework to some extent.

Iterative Solution of Mesh Constrained Optimal Control Problems with Two-Level Mesh Approximations of Parabolic State Equation

We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.

Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √<span style='margin-left:-2px;margin-right:2px;border-top:1px solid black'>N</span>

In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.

联合协方差矩阵重构和ADMM的鲁棒波束形成

为解决传统波束形成器在干扰位置发生扰动和导向矢量失配时,造成自适应权重的不匹配,从而导致算法性能急剧下降,甚至期望信号相消的问题,提出一种联合协方差矩阵重构和交替方向乘子法(Alternating direction method of multipliers,ADMM)的鲁棒波束形成方法。对此,首先基于波束形成器最大输出功率准则,设计了求解最优导向矢量的优化模型。接着,根据Capon算法空间功率谱函数,利用定义的干扰范围对协方差矩阵进行重构,以展宽零陷并增强系统抗运动干扰能力。最后,关于导向矢量的二次不等式约束问题,本质为估计导向矢量和期望导向矢量间的差异,该方法利用ADMM对该二次规划问题进行迭代求解,并在每次迭代中获得导向矢量的具体解。另外,也分析了算法的复杂度。实验结果表明:对比现有的波束形成算法,在干扰处加宽了零陷,提高了波束的抗干扰性;结合复杂度也证明了其计算速度优于现有的算法,并且能够很好地校正失配导向矢量。本方法也为求解二次不等式约束问题和提高波束形成算法性能提供了一种思路和途径。

带有任意弹性支撑的大型有面外支撑杆X撑结构屈曲分析

X型支撑结构已广泛应用于大型海洋工程主要支撑结构设计中,如设计使用不当,将有可能发生由支撑杆的屈曲失稳而引发的结构坍塌变形。在极限荷载下,X撑杆的屈曲失稳本质上属于典型的多跨压杆稳定问题,其极限承载力与撑杆的结构组成、几何参数以及端部约束密切相关。该文主要研究有(无)面外支撑的非对称交叉支撑体系在任意弹性支撑下X撑结构屈曲特性,侧重于考察端部约束、受力形式、面外支撑刚度等因素的影响。首先基于线弹性理论框架,建立了双跨受压杆件平衡方程,利用牛顿迭代算法进行屈曲载荷计算,从而得到跨中连续的非对称交叉支撑杆的有效长度因子数值解,并对端点支撑刚度和跨中支撑刚度进行了敏感性分析。结合工程实践,给出了杆件屈曲长度系数和刚度约束条件关键设计参数。

附加增值条件的移动最小二乘法的点云孔洞修补

由于扫描设备局限或模型结构复杂等因素导致点云模型出现孔洞,这严重影响模型的后续处理。针对点云孔洞的修补问题,文中提出了一种附加增值条件移动最小二乘法的点云孔洞修补方法。首先提取封闭的孔洞边界,通过密度分析进行迭代切片,不仅削弱点云分布不均的影响,还提高模型细节特征的保留程度;再将离散群点投影至拟合曲面,投影点集二次拟合以获取拟合面节点,保证有足够的边界邻域节点为基础进行孔洞修补;最后利用附加增值条件移动最小二乘法对孔洞进行迭代修补,并对增值点云进行曲率约束,从而达到契合原始模型空间特征的重建。实验采用人为在四个点云模型上制造不同类型的孔洞,并与现有的四种方法进行对比,验证所提方法的有效性,结果表明,文中方法相较于现有的四种方法,完整率、准确率提高了1.83%以上,配准均方根误差与平均曲率均方根降低了68%以上,对比证明了文中方法对于点云模型孔洞具有较强的适用性,可为重建三维点云模型提供可靠信息。

Modified Exact Jacobian Semidefinite Programming Relaxation for Celis-Dennis-Tapia Problem

A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.

具有基数约束的多阶段均值-半方差可信性投资组合优化

文章探讨了一个多阶段模糊收益的投资组合优化问题。考虑交易成本、借贷约束、阈值约束和基数约束等现实约束,提出了一种新的多阶段均值-半方差可信性投资组合模型。在该模型中,本文分别运用可信性期望值和半方差来度量投资组合收益和风险。基于可信性理论,将该模型转化为一个动态优化问题。由于存在交易成本和基数约束,该模型是具有路径依赖性的混合整数动态优化问题。本文提出了一种新的离散近似迭代方法进行求解,并证明其线性收敛性。最后,文章运用了具体的算例以验证算法和模型的有效性。

ACG-TypeMethod for InverseQuadratic Eigenvalue Problems in Model Updating of Structural Dynamics

In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M,D and K for the quadratic pencil Q(λ)=λ^(2)M+λD+K,so that Q(λ)has a prescribed subset of eigenvalues and eigenvectors.This method can determine the solvability of the inverse eigenvalue problem automatically.We then consider the least squares model for updating a quadratic pencil Q(λ).More precisely,we update the model coefficient matrices M,C and K so that(i)the updated model reproduces the measured data,(ii)the symmetry of the original model is preserved,and(iii)the difference between the analytical triplet(M,D,K)and the updated triplet(M_(new),D_(new),K_(new))is minimized.In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.

基于近似零范数稀疏恢复的迭代解法的三维重力反演（英文）

重力反演是应用地球物理中一个经典的方法,可以获取地下空间的密度分布特征。本文研究了一种新的三维重力反演方法,以压缩感知中的稀疏恢复方法为基本原理。建立以零范数为约束的目标函数,采用近似零范数求解方法对目标函数进行迭代求解。以重力正演模型为基础进行反演方法研究,建立包含深度加权函数的零范数的目标函数,采用相应的最优化数学方法进行求解,得到稀疏的反演结果。同时,为了得到具有实际地质意义的反演结果,采用惩罚函数将反演密度值约束在具有实际地球物理和地质意义范围内。采用本文提出的反演方法得到的反演目标异常源具有较为清晰的边界、深度信息和剩余密度分布信息。本文利用理论模型实验来验证反演方法效果,并将得到的反演结果与设计的理论模型对比分析说明三维反演方法的有效性和可靠性。为了进一步说明本文采用的反演方法的可靠性,将其应用到美国德克萨斯州采集的实际重力数据反演,并将反演结果与前人研究结果和该地区的测井资料进行对比分析,盐丘的深度为4.2km与测井得到深度4.4km基本上是一致的,说明研究的反演方法具有实际应用价值。

基于非线性预报-校正内点法的电力系统无功优化研究

在非线性原?对偶内点法的基础上引入了预报-校正技术,使改进后的非线性预报-校正内点法获得了较纯原-对偶内点法更大的迭代步长,从而加速了算法的收敛。应用该方法求解电力系统无功优化问题时能有效处理目标函数中的大量不等式约束。IEEE14节点、IEEE30节点、IEEE57节点和IEEE118节点系统的仿真结果表明,该算法收敛快、鲁棒性好。

接触问题有限元分析方法综述

从直接迭代法、接触约束法和数学规划法等方面综述接触问题有限元分析的基本方法 .直接迭代法是一种“试验误差”方法 ,概念清楚 ,实施方便 ,但计算工作量较大 ,而且不能保证迭代一定收敛 .接触约束法主要利用罚函数方法或Lagrange乘子法将接触问题转化为无约束问题求解 .数学规划法利用接触问题的互补条件、非穿透条件等 ,将其归结为二次规划 (线性互补 )问题求解 ,这是一种非迭代类解法 ,收敛平稳、迅速 ,计算工作量较小 .

基于连续过松弛方法的支持向量回归算法(英文)

支持向量回归(support vector regression,简称SVR)训练算法需要解决在大规模样本条件下的凸二次规划(quadratic programming,简称QP)问题.尽管此种优化算法的机理已经有了较为明确的认识,但已有的支持向量回归训练算法仍较为复杂且收敛速度较慢.为解决这些问题.首先采用扩展方法使SVR与支撑向量机分类(SVC)具有相似的数学形式,并在此基础上针对大规模样本回归问题提出一种用于SVR的简化SOR(successive overrelaxation)算法.实验表明,这种新的回归训练方法在数据量较大时,相对其他训练方法有较快的收敛速度,特别适于在大规模样本条件下的回归训练算法设计.