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 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.

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.

An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints

This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.

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.

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.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.

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.

PROJECTED GRADIENT DESCENT BASED ON SOFT THRESHOLDING IN MATRIX COMPLETION

Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.

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 projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem

Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

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.

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

Driven by the increase in CO_(2)concentration,climate models reach a consensus that the large-scale circulation of the South Asian summer monsoon(SASM) becomes weakened but with different magnitudes.This study investigates the major uncertainty sources of the SASM response to an abrupt quadrupling of CO_(2)(abrupt-4×CO_(2))in 18 models of phase 6 of the Coupled Model Intercomparison Project.The projected weakening of the SASM indicated by both zonal and meridional monsoon circulation indices is closely linked to decreases in the meridional gradient of upper-tropospheric temperature between Eurasia and the Indian Ocean(EUTT-IUTT).A climate feedback-response analysis method is applied to linearly decompose the uncertainty of changes in EUTT-IUTT into the partial changes due to external forcing and internal processes of the earth-atmosphere column.Results show that the uncertainty of changes in EUTT-IUTT is contributed positively by the dominant atmospheric dynamic process,followed by the cloud shortwave radiative effect,and negatively by the surface latent heat flux and cloud longwave radiative effect.Contributions from CO_(2)forcing and other internal processes including albedo and water vapor feedbacks,oceanic heat storage,and sensible heat flux are found to be minor.

中吉乌铁路吉国境内段限制坡度方案研究

研究目的:中吉乌铁路吉尔吉斯斯坦境内段位于天山山系南天山的西部,穿越莫尔多套山、费尔干纳山,线路跨越吐尔尕特高山区、阿尔帕高原盆地区等10个地貌单元,线路附近最高点贾曼达万山高程4 205 m,最低点贾拉拉巴德高程722 m,相对高差3 483 m,地形高差巨大,工程地质条件复杂,吐尔尕特至马克马尔段采用1 435 mm标准轨距、马克马尔至贾拉拉巴德南段采用1 520 mm宽轨距,线路限制坡度的选择是项目研究的重点和难点。研究结论:(1)结合线路沿线地形地质条件、承担运输货物特点、列车牵引质量、机车选型、工程投资和综合经济性,对限制坡度分段进行研究;(2)标轨段重点对18‰、20‰、24‰、25‰四个方案,宽轨段重点对18‰、20‰、24‰、27‰四个方案进行了分析研究,为降低工程投资、提高项目经济性、匹配运输组织、优化运输条件、保障运营安全性,推荐中吉乌铁路吉国境内段限制坡度采用20‰方案;(3)本研究思路和方法可为境外铁路工程建设提供参考和借鉴。

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

基于可移动单元的智能反射面辅助近场定位技术

RIS在提高感知系统可靠性方面具有广泛的应用前景。同时,可移动天线技术可以利用天线的局部运动,动态地改变发射机和/或接收机处的天线位置,以优化信道条件,提高通信性能。因此,将可移动天线技术引入RIS,通过充分利用无线信道在有限区域的空间变化,进一步实现智能可控的无线信道传播环境。基于此,研究了一种基于可移动单元的智能反射面辅助近场定位技术。首先,提出了基于近场模型的最大似然定位算法,并推演出衡量定位性能的CRLB。然后,提出了一种基于投影梯度下降的交替优化算法,实现智能反射单元动态位置和波束赋形的联合优化,以获得RIS用于定位的优化结构和相位配置。仿真结果表明,与传统固定单元的RIS相比,通过灵活调整RIS反射单元的拓扑结构,获得更好的信道条件,能够显著降低用户位置估计的CRLB,提高系统的定位性能。

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。

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。

中国退耕还草的土壤碳固持效应及影响因素

基于检索1950-2016年发表在中国知网、Google Scholar、Web of Science等数据库的文章,筛选出关于我国退耕还草工程与土壤有机碳的文献123篇(126个研究地点)。基于筛选文献,提取了农田和恢复草地的土壤有机碳含量、土壤有效养分含量、恢复时间和气候等数据735条,旨在探究我国退耕还草工程对土壤有机碳含量的影响及其主导因素。结果表明:1)农田恢复为草地后,土壤有机碳含量呈先下降后上升趋势(时间拐点约为第6年),整体上退耕还草工程使土壤有机碳含量提高了19.8%。2)土壤有机碳的正响应随土壤深度增加而减弱,且深度超过1 m时其正响应不明显。3)土壤有效氮是影响土壤有机碳恢复的主要因素,而土壤有效磷和植物功能群对其影响不大。4)沿着增加的水分梯度,土壤有机碳的恢复效果由负变正,转变阈值为25.15 (干旱指数)。总体而言,我国退耕还草工程对土壤有机碳含量的影响为正效应,此效应受环境梯度和恢复时间的共同影响。本研究能够为我国土地利用变化背景下土壤碳库管理的相关决策提供科学依据。