High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

NEW HYBRID CONJUGATE GRADIENT METHOD AS A CONVEX COMBINATION OF LS AND FR METHODS

In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

NEWTON METHOD FOR SOLVING A CLASS OF SMOOTH CONVEX PROGRAMMING

An algorithm for solving a class of smooth convex programming is given. Using smooth exact multiplier penalty function, a smooth convex programming is minimized to a minimizing strongly convex function on the compact set was reduced. Then the strongly convex function with a Newton method on the given compact set was minimized.

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.

Fast First-Order Methods for Minimizing Convex Composite Functions

Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.

基于机器视觉的芯片字符区域分割和定位算法

芯片表面的字符对分选具有重要意义,对字符的定位是分选工作的关键步骤。为了提高分选工作定位效率和定位精度,提出了一种基于改进的区域生长算法和凸包检测算法分割和定位芯片表面字符区域方法。首先,对采集图像进行预处理操作,利用改进的Canny算法获取无干扰图像边缘,将图像边缘作为区域生长法的种子点并以图像自适应阈值作为生长准则分割图像,使用最大内接矩形算法粗定位字符区域;其次,采用Harris角点检测算法获取字符角点分布位置;最后,筛选角点并提取关键点,利用一种改进的凸包检测算法定位字符区域。经过实验验证,所设计的算法能够完整的分割和定位芯片表面字符区域,定位精度和效率较原有方法提升5.3%和15.4%,满足实际工业生产的要求。

A Regularized Newton Method with Correction for Unconstrained Convex Optimization

In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC2, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.

交错凸齿式宽苗带小麦精量排种器设计与试验

针对外槽轮式小麦宽苗带排种器排量不稳定和苗带内种子分布均匀性较差的问题,该研究设计了一种交错凸齿式宽苗带小麦精量排种器。通过连续充种分析和排量计算,确定凸齿高度和凸齿角度是影响排量一致性和排种均匀性的关键参数。应用离散元法对上述关键参数进行中心旋转组合仿真试验,结果表明,对排量一致性、排种均匀性影响显著性程度由大到小的因素分别依次为凸齿角、凸齿高、作业速度,且均具有交互影响。借助响应面分析,得出凸齿高5 mm、凸齿角75°时的排量一致性和排种均匀性较优,平均变异系数分别为2.27%和7.61%。对该参数组合排种器进行样机试制,并进行台架试验,台架试验结果表明,排种一致性和均匀性变异系数与仿真值误差均低于5%,说明仿真优化结果可靠、准确。田间对比试验结果表明,播量120、150和180 kg/hm~2时,交错凸齿式宽苗带小麦精量排种器的播量一致性、纵向播种均匀性和横向播种均匀性变异系数分别较外槽轮式排种器降低0.99、3.01和9.38个百分点,满足小麦宽苗带播种农艺要求。研究结果可为提高排种均匀性的小麦排种装置设计提供参考。

一种连续型不确定性复杂系统博弈理论及算法研究

当前对于不确定性复杂系统博弈的研究,通常情况下有关策略集是离散的,而非连续和随机的。而在复杂经济社会系统中,常常会遇到连续性随机博弈问题,以及系统中数据的确权问题。在此背景下,提出了一种随机博弈的概念,给出连续策略集下N人非合作随机博弈模型均衡解存在性定理,以及复杂信息系统随机博弈模型的构建及其纳什均衡解算法。给出连续策略下不确定性N人非合作随机博弈概念,建立以局中人的最大收益为目标函数的N人非合作随机博弈模型,提出了均衡解的存在性定理;构建了Wasserstein模糊集,之后融合分布鲁棒优化方法以及投资组合优化方法将该模型转化为有限凸规划,并运用遗传算法求解局中人的近似混合策略,最后构建了基于回归分析的纳什均衡求解算法并将纳什均衡解归一化进行确权。实证分析表明,所构建的理论与算法是有效可行的。

团聚物与凸起结构柔性振动筛板碰撞解聚特性

为了促进潮湿细粒煤团聚物的解聚,提出将凸起结构筛板用于物料的筛分。首先,采用挤压壁面法构建了潮湿细粒团聚物模型,仿真分析了团聚物在不同筛板上的碰撞解聚过程及解聚程度;其次,通过单因素和响应面分析法研究了凸起结构参数对团聚物碰撞解聚程度的影响性能,对凸起结构参数进行了优化;最后,通过筛分试验对比了物料在普通筛板和凸起结构筛板的解聚性能。结果表明:凸起结构能提高潮湿细粒团聚物的解聚程度,其参数对团聚物的解聚性能有显著影响;平均垂直应力σyy、液桥断裂百分比DR、平均偏心距离Ad和膨胀速度Ue随凸起结构下底a、上底b的增加呈非单调变化,与高h的变化呈正比;响应面分析得到凸起结构各参数对解聚程度的影响显著性依次为h>b/a>a;通过对凸起结构参数优化,团聚物的解聚程度最高可提升13.4%。

基于复合正则化的稀疏SAR成像方法研究

随着高分辨率对地观测要求的不断提高,合成孔径雷达(Synthetic Aperture Radar,SAR)的应用将越来越广泛。针对高分辨率SAR成像存在数据量大、存储难度高、计算时间长等问题,目前常用的解决方法是在SAR成像模型中引入压缩感知(Compressed Sensing,CS)的方法降低采样率和数据量。通常使用单一的正则化作为约束条件,可以抑制点目标旁瓣,实现点目标特征增强,但是观测场景中可能存在多种目标类型,因此使用单一正则化约束难以满足多种特征增强的要求。本文提出了一种基于复合正则化的稀疏高分辨SAR成像方法,通过压缩感知降低数据量,并使用多种正则化的线性组合作为约束条件,增强观测场景中不同类型目标的特征,实现复杂场景中高分辨率对地观测的要求。该方法在稀疏SAR成像模型中引入非凸正则化和全变分(Total Variation,TV)正则化作为约束条件,减小稀疏重构误差、增强区域目标的特征,降低噪声对成像结果的影响,提高成像质量;采用改进的交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现复合正则化约束的求解,减少计算时间、快速重构图像;使用方位距离解耦算子代替观测矩阵及其共轭转置,进一步降低计算复杂度。仿真和实测数据实验表明,本文所提算法可以对点目标和区域目标进行特征增强,减小计算复杂度,提高收敛性能,实现快速高分辨的图像重构。

基于点估计仿射可调鲁棒优化的含储能电力系统实时调度

为应对大规模风电的接入,建立一种机组与储能联合参与自动发电控制的电力系统实时调度模型,并提出一种点估计仿射可调鲁棒优化来处理风电不确定性。不同于传统仿射可调鲁棒调度优化基准运行成本,点估计仿射可调鲁棒调度优化期望运行成本以提高系统经济性。提出利用确定性的点估计法来实现对期望运行成本的快速、精确评估。所提模型为一混合整数双线性约束问题,采用一种“预估-矫正”的凸化方法来求解该难题,预估阶段对储能的状态变量进行松弛,而矫正阶段直接对其状态变量进行矫正。最后,引入一种凸函数差优化进一步凸化2个阶段的双线性约束问题,以提高含储能实时调度的求解质量。在IEEE39、118以及300节点3个系统的仿真验证了所提模型及方法的有效性。

线性化严格收缩的Peaceman-Reachford分裂方法

考虑具有线性约束的三块可分凸优化问题,在改进的严格收缩可分离的凸最小化模型分裂法(MSC-PRSM)的基础上,将原始问题的y-子问题和z-子问题的目标函数分别在y^(k)和z^(k)处进行线性化,并增加一个邻近项,使线性化的MSC-PRSM子问题更容易求解,降低了计算量,从计算时间角度比MSC-PRSM更有优势,并证明了新算法的收敛性.

火星表面上升轨迹映射伪谱凸优化方法

针对火星表面上升轨迹优化问题,提出了映射Chebyshev伪谱凸优化方法。首先采用无损凸化方法对火星表面上升燃耗最优问题进行凸松弛,然后将凸化后的问题在映射Chebyshev-Gauss-Lobatto点处离散,利用重心有理Lagrange插值技术进行插值,最后使用序列凸优化方法迭代求解,得到数值最优解。仿真对比了本文方法、一般伪谱凸优化方法和经典的序列凸优化方法,证明了本文方法在计算效率方面存在优势,并有效改善了标准Chebyshev微分矩阵的病态特性。

基于显著性引导的保凸性水平集分割算法

结合彩色眼底图像中视神经盘的解剖学特征,引入零水平集曲线的曲率变化来优化活动轮廓模型,提出了一种全自动分割视神经盘的水平集算法CRLSF。该算法利用显著性算法快速获取初始轮廓,且该初始轮廓与视神经盘轮廓非常接近,大幅度提高分割效率。采用保凸机制能够使得曲线在演化过程中不受到视神经盘周围毛细血管的影响以保持分割曲线的凸性。最后,在迭代中引入目标函数来评估算法的收敛性。实验表明,提出的CRLSF算法优于已有的算法。

含椭圆算子的反射随机偏微分方程

本文考虑一类含椭圆算子的多维反射随机偏微分方程,其解被限制在一个有界凸区域内.本文将利用惩罚法建立其解的存在唯一性定理.

部分线性空间自回归模型的惩罚最小二乘方法

部分线性空间自回归模型因具有参数空间自回归模型的解释能力和非参数空间自回归模型的灵活性而成为一类备受关注的半参数空间自回归模型。主要研究部分线性空间自回归模型的变量选择问题,基于轮廓拟最大似然方法和一类非凸罚函数,提出了一类惩罚最小二乘方法同时选择该模型的参数部分中重要解释变量和估计相应的非零回归系数。在适当的正则条件下,推导了回归系数的惩罚估计的收敛速度,并证明了所提出的变量选择方法具有Oracle性质。模拟研究和实际数据分析均表明所提出的变量选择方法具有满意的有限样本性质。

基于改进颜色线模型的水下图像增强算法

为解决水下设备采集图像存在的雾化和颜色失真等退化问题,提出一种基于改进颜色线模型的水下图像增强方法。首先,提出一种基于改进四叉树细分的水下背景光估计方法,消除水下因素的干扰,得到更加准确的背景光估计值。其次,建立基于颜色线规律的局部透射率优化模型,并设计一种新的Gauss-Seidel型交替线性极小化(Gauss-Seidel Type Inertial Proximal Alternating Linearized Minimization Algorithm,GiPALM)非凸优化方法求解透射率,在提高模型收敛速度的同时得到更加准确的透射率估计值。最后,在背景光和透射率估计得到恢复图像的基础上,进一步采用线性拉伸校正图像的颜色信息,得到符合人眼感官视觉的水下增强图片。实验结果表明,本文方法在主观评价、客观评价、颜色准确度和应用测试等方面均优于其他先进算法,展现了出色的性能,有效提高了水下图像的清晰度和可视性。