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.

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.

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.

A Probe Method of Gradient Projection Type

In this paper,a probe method for nonlinear programming wiht equality and inequality is given. Its iterative directions at an arbitrary point x can be obtained through solving a liear system. The terminate conditions and choices of the parameters are given. The global convergence of the method is proved. Further more,some well known gradient projection type algorithms [1-15] and new gradient projection type algorithms from the linear system are given in this paper.

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.

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

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

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.

Monotone projected gradient methods for large-scale box-constrained quadratic programming

Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.

Efficient projected gradient methods for cardinality constrained optimization

Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constrained optimization problems, which involves box constraints and a singly linear constraint. An efficient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projection subproblem. Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems. Global convergence of the methods is established under suitable assumptions. Finally, we illustrate some applications of the proposed methods for signal recovery and index tracking.Especially for index tracking, we propose a new model subject to an adaptive upper bound on the sparse portfolio weights. The computational results demonstrate that the proposed projected gradient methods are efficient in terms of solution quality.

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 pressure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equations.The existence and uniqueness of the solution and the optimal error estimates are proved.

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.

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.

Uncertainty in projections of the South Asian summer monsoon under global warming by CMIP6 models:Role of tropospheric meridional thermal contrast

本文基于第六次国际耦合模式比较计划共18个模式的工业革命前实验和CO_(2)浓度突然四倍实验,发现在CO_(2)四倍强迫下,南亚夏季风环流呈显著减弱趋势,但减弱强度存在较大模式间差异.利用Webster-Yang指数和经向哈得莱环流指数的下降趋势表征SASM减弱强度,发现该下降趋势与欧亚大陆-印度洋之间对流层上层经向温度梯度的变化值(EUTT-IUTT)高度相关.进一步利用气候反馈-响应分析方法进行分析,发现EUTT-IUTT变化的模式间差异主要来自于大气动力过程,其次是云的短波辐射效应的贡献.地表潜热通量和云的长波辐射效应缩小了EUTT-IUTT变化的模式间差异.

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。

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.

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。

带有CVaR罚的分布鲁棒指数跟踪模型:易求解的转化

提出了一种带有条件在险价值(CVaR)惩罚的分布鲁棒指数跟踪模型,该模型将分布鲁棒优化的思想与CVaR惩罚相结合。模型中概率的不确定性通过随机向量的一阶和二阶矩的置信区域来描述。将该模型由一个“min-max-min”形式的优化问题,等价转化为一个非光滑最小化问题。同时提供了一个近似求解带有连续型随机向量的非光滑极小化问题的离散化方案,通过该方案离散化之后的目标函数包含众多但有限个的非光滑函数的最大化。在较弱的条件下证明了离散化之后的模型收敛到原问题等价转化后的非光滑连续分布模型。采用了光滑投影梯度(Smoothing Projected Gradient,SPG)方法求解离散化后的模型,并证明了由SPG方法产生的迭代点序列的任何聚点都是离散化之后模型的全局最小值点。在2008年1月至2023年7月的纳斯达克日度指数数据集上与先进模型进行比较,数值结果验证了所提模型以及SPG方法的有效性。