A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

A NEW GRADIENT PROJECTION METHOD AND ITS CONVERGENCE

In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.

An Efficient Projected Gradient Method for Convex Constrained Monotone Equations with Applications in Compressive Sensing

In this paper, a modified Polak-Ribière-Polyak conjugate gradient projection method is proposed for solving large scale nonlinear convex constrained monotone equations based on the projection method of Solodov and Svaiter. The obtained method has low-complexity property and converges globally. Furthermore, this method has also been extended to solve the sparse signal reconstruction in compressive sensing. Numerical experiments illustrate the efficiency of the given method and show that such non-monotone method is suitable for some large scale problems.

A Spectral Projected Gradient-Newton Two Phase Method for Constrained Nonlinear Equations

In this paper, we proposed a spectral gradient-Newton two phase method for constrained semismooth equations. In the first stage, we use the spectral projected gradient to obtain the global convergence of the algorithm, and then use the final point in the first stage as a new initial point to turn to a projected semismooth asymptotically newton method for fast convergence.

Projected gradient trust-region method for solving nonlinear systems with convex constraints

In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

ANonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets

In this work we consider an extension of the classical scalar-valued projected gradient method for multiobjective problems on convex sets.As in Fazzio et al.(Optim Lett 13:1365-1379,2019)a parameter which controls the step length is considered and an updating rule based on the spectral gradient method from the scalar case is proposed.In the present paper,we consider an extension of the traditional nonmonotone approach of Grippo et al.(SIAM J Numer Anal 23:707-716,1986)based on the maximum of some previous function values as suggested in Mita et al.(J Glob Optim 75:539-559,2019)for unconstrained multiobjective optimization problems.We prove the accumulation points of sequences generated by the proposed algorithm,if they exist,are stationary points of the original problem.Numerical experiments are reported.

Discontinuous element pressure gradient stabilizations for compressible Navier-Stokes equations based on local projections

A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.

A SUBSPACE PROJECTED CONJUGATE GRADIENT ALGORITHM FOR LARGE BOUND CONSTRAINED QUADRATIC PROGRAMMING

A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.

天基信息支援体系建模与效能评估方法

针对天基信息支援体系效能评估中存在的主观性强与复杂性高的问题,提出一种基于投影梯度神经网络的天基信息支援体系效能评估方法。首先,基于国防部体系框架(Department of Defense Architecture Framework,DoDAF)视图产品与包以德循环(observation,orientation,decision,action,OODA)梳理体系作战流程,进而建立评估指标体系,并基于离散事件仿真生成效能评估数据样本。然后,基于Rosen-反向传播(back propagation,BP)神经网络构建效能评估代理模型,并通过对权重参数的限制来解决在效益型指标下评估模型难以解释的问题。最后,对仿真样本进行评估模型验证试验,结果表明所提方法在天基信息支援体系效能评估中相较于传统BP神经网络计算性能提升超过50%,能够为天基信息支援体系效能评估提供技术支撑。

两阶段非负矩阵分解算法及其在光谱解混中的应用

非负矩阵分解问题(nonnegative matrix factorization,NMF)模型已成功应用至高光谱遥感影像处理中的光谱解混工作,由于NMF优化模型具有多个局部极小点,使得分解结果不稳定。设计初始化方法或者选择带正则项的问题模型是提高分解精度的两种常用方法。本文提出了两阶段的NMF算法,实现了初始点选取和正则项设计的结合。第一阶段借助k-均值获得k个聚类中心,给出迭代的初始点;利用第一阶段的初始矩阵U^(0),定义了针对端元矩阵的正则项‖U-U^(0)‖_(F)^(2),第二阶段采用基于交替非负最小二乘框架的投影梯度算法,求解新的正则化NMF问题。正则项中的端元初始矩阵U^(0)除了采用k-均值获得k个聚类中心,也可采用真实地物光谱,它的引入提高了算法的灵活度。数值结果表明新算法更加稳定,且分解的精确性有效提高。

梯度投影法实现永磁同步电机最优曲线跟踪

针对永磁同步电机弱磁控制在线计算复杂度高、计算负担较重的问题,提出一种高效的弱磁曲线跟踪方法,以实现永磁同步电机的运动控制,通过一种更优化的投影与迭代结合的方法实现在一定的电流、电压约束下,电机最优运行状态的在线跟踪。同时,提出了针对ADADELTA梯度下降法的一种简化方法,优化了梯度下降法的计算流程,减少了迭代次数,提高了运算性能。该方法避免了不同运行区域的算法切换,有效地发挥了电机潜能,保证电机高功率输出。最后通过电机对拖实验,验证了此算法的合理性。

基于自适应闭环反馈的高空车臂架避障控制研究

针对改进梯度投影法在混合式高空作业车应用中出现的速度、轨迹不连续以及避障过程中末端速度突变等问题,提出了一种基于自适应闭环反馈的高空车臂架避障控制算法。对改进梯度投影法进行优化,实现了存在伸缩臂的高空车臂架与末端的速度、轨迹连续的运动控制。采用伪距离描述臂架与障碍物的接近程度,对传统避障速度算法进行优化,并提出一种自适应闭环反馈方法,将反馈权重与伪距离相关联,使反馈权重自适应变化。所提算法在保证末端轨迹精度的同时大大改善了臂架关节在避障过程中的速度突变。仿真及半物理实验结果表明,相较于传统方法,所提方法速度变幅大大减小且轨迹更加平滑,实现了多障碍物避障与同一障碍物多次避障。

A Framework of Convergence Analysis of Mini-batch Stochastic Projected Gradient Methods

In this paper,we establish a unified framework to study the almost sure global convergence and the expected convergencerates of a class ofmini-batch stochastic(projected)gradient(SG)methods,including two popular types of SG:stepsize diminished SG and batch size increased SG.We also show that the standard variance uniformly bounded assumption,which is frequently used in the literature to investigate the convergence of SG,is actually not required when the gradient of the objective function is Lipschitz continuous.Finally,we show that our framework can also be used for analyzing the convergence of a mini-batch stochastic extragradient method for stochastic variational inequality.

A LEVEL SET METHOD FOR MICROSTRUCTURE DESIGN OF COMPOSITE MATERIALS

Based on a level set model and the homogenization theory, an optimization al- gorithm for ?nding the optimal con?guration of the microstructure with speci?ed properties is proposed, which extends current research on the level set method for structure topology opti- mization. The method proposed employs a level set model to implicitly describe the material interfaces of the microstructure and a Hamilton-Jacobi equation to continuously evolve the ma- terial interfaces until an optimal design is achieved. Meanwhile, the moving velocities of level set are obtained by conducting sensitivity analysis and gradient projection. Besides, how to handle the violated constraints is also discussed in the level set method for topological optimization, and a return-mapping algorithm is constructed. Numerical examples show that the method exhibits outstanding ?exibility of handling topological changes and ?delity of material interface represen- tation as compared with other conventional methods in literatures.

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.

改进模型预测控制的农机轨迹跟踪算法研究

针对无人驾驶农机进行轨迹跟踪时精度与稳定性较差的问题,提出了一种基于模型预测控制(MPC)的轨迹跟踪方法。首先,建立农机车辆的运动学模型,利用粒子滤波对农机状态量进行估计来提高农机的定位精度;其次,在设计MPC控制器时引入了梯度投影算法,该算法相比于传统有效集算法减少了迭代步数,具有更快的收敛速度,提高了农机进行跟踪控制时的计算效率;最后,在淄博市某无人农场进行了农机轨迹跟踪试验。结果表明:该方法可以实现良好的跟踪控制精度,符合精准农业的作业要求。

南水北调东线梁济运河段输水流量损失的经验估算方法

传统Kostiakov经验公式计算结果为一定值,在未衬砌的沿程地质变化较大的河段应用时不能充分体现输水损失沿程变化的动态特点。为克服原公式局限性,采用积分学方法及广义简约梯度法对Kostiakov经验公式进行改进,形成改进Kostiakov经验公式法,并以南水北调东线梁济运河段为例,利用2013—2019年实测数据,对改进Kostiakov经验公式中的参数进行率定。考虑梁济运河段运行期间易受春灌影响,分别利用受春灌影响显著的2019—2020年和影响一般的2020—2021年实测数据对改进Kostiakov经验公式进行验证。结果表明:改进Kostiakov经验公式法可克服原公式应用时的局限性,有效提升输水损失计算精度,扩大原公式的应用范围;改进后计算结果与两个时段实测数据的平均相对误差分别由原来的27.26%和11.72%降低为7.9%和6.84%,对调水工程运行调度具有重要意义。

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

点至平面代数曲线正交投影计算的混合算法

点至平面代数曲线的正交投影计算在计算机图形学、计算机辅助几何设计领域,特别是交互式设计等应用中有着非常重要而广泛的运用.基于牛顿梯度下降法、切线和曲率圆形成中点的中点脚点法,以及混合几何加速正交法的计算方法,提出一种混合算法用于计算点到平面代数曲线的正交投影问题.首先,采用牛顿梯度下降法使初始迭代点落在平面代数曲线上;其次,利用切线和曲率圆所形成的中点作为脚点,再结合牛顿梯度下降法,将落在平面代数曲线上的迭代点逐渐挪动至正交投影点很靠近位置;最后,使用混合几何加速正交法得到正交投影点.采用3个封闭平面代数曲线实例进行实验,通过收敛性计算验证,结果表明当测试点比较远或代数曲线次数比较高时,该算法是鲁棒和高效的.