Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional

First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.

Design and analysis of an advanced thermal management system for the solar close observations and proximity experiments spacecraft

In this paper,the mission and the thermal environment of the Solar Close Observations and Proximity Experiments(SCOPE)spacecraft are analyzed,and an advanced thermal management system(ATMS)is designed for it.The relationship and functions of the integrated database,the intelligent thermal control system and the efficient liquid cooling system in the ATMS are elaborated upon.For the complex thermal field regulation system and extreme space thermal environment,a modular simulation and thermal field planning method are proposed,and the feasibility of the planning algorithm is verified by numerical simulation.A solar array liquid cooling system is developed,and the system simulation results indicate that the temperatures of the solar arrays meet the requirements as the spacecraft flies by perihelion and aphelion.The advanced thermal management study supports the development of the SCOPE program and provides a reference for the thermal management in other deep-space exploration programs.

Fast Tensor Principal Component Analysis via Proximal Alternating Direction Method with Vectorized Technique

This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.

A note on a family of proximal gradient methods for quasi-static incremental problems in elastoplastic analysis

Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.

A New Inexactness Criterion for Approximate Logarithmic-Quadratic Proximal Methods

Recently,a class of logarithmic-quadratic proximal(LQP)methods was intro- duced by Auslender,Teboulle and Ben-Tiba.The inexact versions of these methods solve the sub-problems in each iteration approximately.In this paper,we present a practical inexactness criterion for the inexact version of these methods.

Comparison of two approximal proximal point algorithms for monotone variational inequalities

Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as predic- tion-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm I; in the same way, Algorithm II is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm II usually outperforms Algorithm I. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm II to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some nu- merical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

基于误差幅空特性分析的空间负荷预测误差评价方法

对空间负荷预测误差进行有效评价是客观认识预测结果,指导预测结果合理应用的前提。然而,现有空间负荷预测误差评价的研究存在对误差的空间分布不考虑或考虑不充分导致评价不准确的问题。为此,提出一种基于误差幅空特性分析的空间负荷预测误差评价方法。首先,从空间负荷预测误差幅值大小和空间分布对电网规划影响的角度出发,对误差的幅空特性进行详细分析;其次,利用运输问题的数学模型来表征正负误差的幅空抵消特性,使用各空间邻近度–幅值误差值曲线与x轴围成面积之和来表征剩余未抵消误差的幅空叠加特性;然后,分别通过伏格尔法和各梯形面积累加公式来计算正负误差的幅空抵消影响值和剩余未抵消误差的幅空叠加影响值,并在此基础上构建空间负荷预测误差评价指标;最后,基于误差对电网规划的实际影响给出对误差评价指标性能的检验方法。算例分析表明,与传统方法相比,该文所提误差评价方法从幅值和空间两个维度实现了对空间负荷预测误差更为全面的评估,与误差对电网规划影响的实际情况贴近度更高。

基于倾向性评分匹配法探讨血府逐瘀汤对老年股骨粗隆间骨折患者PFNA术后康复的影响

目的:基于倾向性评分匹配法探讨血府逐瘀汤对老年股骨粗隆间骨折患者PFNA术后康复的影响。方法:回顾性分析140例行防旋股骨近端髓内钉(proximal femoral nail antirotation,PFNA)手术治疗的股骨粗隆间骨折患者,使用SPSS 22.0进行倾向性匹配评分匹配分为观察组(血府逐瘀汤治疗)和对照组(常规支持治疗)各50例,比较两组术后相关康复治疗指标,并对两组用药安全性进行评价分析。结果:观察组证候积分,术后第5、7天患肢肿胀程度,VAS评分,术后第3、7天血清白细胞及C反应蛋白水平均明显低于对照组(P<0.05),而术后第7天血清血红蛋白、红细胞压积水平和术后1个月Harris评分均显著高于对照组(P<0.05);两组不良反应发生率比较,差异无统计学意义(P>0.05)。结论:PFNA联合血府逐瘀汤内服治疗对老年股骨粗隆间骨折术后康复恢复效果确切,可显著减轻患肢肿胀程度,在更短时间内缓解患者局部疼痛,减少术后隐性失血,提升Harris评分,快速恢复髋关节功能,且不增加患者用药安全性风险。

基于压缩感知的缺失机械振动信号重构新方法

针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。

近端不良锚定区Stanford B型主动脉夹层介入治疗方式的研究进展

近端不良锚定区Stanford B型主动脉夹层介入治疗方式主要包括弓上分支动脉重建和非弓上分支动脉重建技术。弓上分支动脉重建技术相对于非弓上分支动脉重建技术有较低的不良事件发生率。弓上分支动脉重建介入治疗方式有多种,不同的介入治疗方式对胸主动脉腔内修复术疗效亦产生不同的影响。本文就不同介入治疗方式进行综述分析,为了更深入地分析和总结不同介入治疗方式对近端不良锚定区Stanford B型主动脉夹层的优、劣势和临床效果,以便为临床手术决策提供可行的参考依据。

酶介导的邻近细胞标记方法探究细胞间相互作用

细胞-细胞相互作用(cell-cell interactions,CCIs)可以通过细胞表面蛋白质、聚糖、脂质等介导的细胞间突触形成而发生,以维持机体稳态和调控生理功能。这些CCIs是复杂的,涉及许多不同的细胞表面和细胞内分子的参与。随着基础研究和转化医学的不断发展,如何准确识别细胞间相互作用并对其进行表征和定量,引起了广泛关注。近年来,研究CCIs的技术手段不断推陈出新,而邻近标记是一种十分有前景的研究细胞间相互作用的化学生物学方法。目前,主要有两种类型的标记策略。一种是依赖基因工程操作,在“诱饵”细胞表面表达外源酶,通过其与相邻细胞上的受体底物的直接结合,以便发生细胞间邻近标记。另一种是使用酶或小分子催化剂(例如光催化剂),通过基因工程重组表达或借助化学(化学酶)方法将它们偶联在“诱饵”细胞表面,在适当的刺激或激活后,靶向递送感兴趣的标记分子,实现邻近标记。其中,酶介导的邻近细胞标记方法在检测和表征CCIs上具有重要的应用价值。该综述将标记过程中涉及有酶参与的方法定义为酶介导的邻近细胞标记方法,这种方法的一个明显优势是,由于酶和受体底物之间直接的物理接触或酶催化产生高反应活性标记分子而实现小的标记半径范围。该综述旨在归纳与总结近年来开发的酶介导的邻近细胞标记方法的原理、优缺点及现有应用。

煤矿采掘面隐患排查治理效果评价研究

基于袁店二井煤矿生产,全面的隐患排查治理对于避免事故发生、提高矿井生产效率和优化矿井安全管理而言有重要的作用。为预防事故发生,消除安全隐患,建立了评价指标体系,利用AHP法确定各级指标的权重,结合煤矿现场实际情况,由三位专家现场打分,利用TOPSIS法构造评价矩阵,计算出影响煤矿采掘面隐患排查治理效果指标的综合得分,得到6个一级指标下影响隐患排查治理效果最显著的6个二级指标,并提出相应的治理效果评价体系,该体系适用于常规煤矿采掘面的隐患排查及治理。

面向信息系统推荐与决策的高阶张量分析方法

张量数据(或多维数组)在各个行业的信息系统中广泛存在,例如医疗系统中的功能性磁共振成像(fMRI)数据和商品数据信息系统中的用户-产品数据.将这些数据用以预测张量特征与单变量响应之间的关系,可以实现数据赋能,提供更精准的服务或解决方案,例如疾病决策诊断或商品推荐.然而,现有的张量回归方法存在2个主要问题:一是可能丢失了张量的空间信息,导致预测结果不准确;二是计算成本过高,导致服务或解决方案不及时.对于具有高阶结构的大规模数据而言,这2点则显得更为突出.因此为了实现数据赋能,即利用张量数据来提高信息服务或解决方案的质量和效率,提出了稀疏低秩张量回归模型(sparse and low-rank tensor regression model,SLTR).该模型通过对张量系数应用l1范数和张量核范数使得张量系数具有稀疏性和低秩性两大特点,这样既保留了张量的结构信息又可以方便地解释数据.利用近端梯度方法优化了混合正则化器,使得求解过程可扩展且高效.除此之外证明了SLTR的严格误差界.在多个模拟数据集和一个视频数据集上的实验结果表明,SLTR相比于之前的方法,在更短的时间内获得了更好的预测性能.

一种基于稀疏优化和Nesterov动量策略的模型剪枝算法

随着深度学习快速发展,模型的参数量和计算复杂度爆炸式增长,在移动终端上部署面临挑战,模型剪枝成为深度学习模型落地应用的关键。目前,基于正则化的剪枝方法通常采用L2正则化并结合基于数量级的重要性标准,是一种经验性的方法,缺乏理论依据,精度难以保证。受Proximal梯度方法求解稀疏优化问题的启发,本文提出一种能够在深度神经网络上直接产生稀疏解的Prox⁃NAG优化方法,并设计了与之配套的迭代剪枝算法。该方法基于L1正则化,利用Nesterov动量求解优化问题,克服了原有正则化剪枝方法对L2正则化和数量级标准的依赖,是稀疏优化从传统机器学习向深度学习的自然推广。在CIFAR10数据集上对ResNet系列模型进行剪枝实验,实验结果证明Prox⁃NAG剪枝算法较原有剪枝算法性能有所提升。

一种基于层接近度和分支距离函数的最优个体选择算法

文章针对目前最优个体评价及选择时存在的问题,在综合分析层接近度和分支距离函数特点的基础上,提出一种层接近度和分支距离函数联构的测试用例评价算法。该算法的基本思路是,在进化过程中选择领航个体时,先选择实际执行路径与目标路径接近度高的个体,再在这些个体集中选择分支距离最小的个体,从而得到领航能力最优的个体。实验结果表明,所提算法能快速寻优到测试用例,尤其是针对多层嵌套程序的测试用例,生成表现良好。

脉冲负载下柴油发电机组建模优化与评价

针对柴油发电机组-三相不控整流器-DC/DC变换器-脉冲负载系统中柴油发电机组的输出特性,提出仿真模型与试验电源输出电压(流)波形契合度的评价指标,以判断模型的仿真程度;提出了基于反向(BP)传播神经网络算法的同步发电机励磁电压输出动态限幅方法,应用于脉冲负载下柴油发电机组的模型优化。试验验证表明:27组算例中,初始仿真模型有18组波形实时契合度值不足90%,优化仿真模型27组值均大于90%。说明本文提出的优化方法使仿真模型比初始模型更加有效,可应用于后续柴油发电机组带脉冲负载系统的研究。

近距离矿山法隧道施工既有地铁结构保护技术研究

暗挖隧道施工平行近接既有地铁隧道影响较大,如何保障平行近接既有结构安全是未来发展趋势。以广州地铁11号线中山八站工程施工为背景,通过数值模拟计算暗挖隧道平行施工对邻近既有5号线影响,进而提出了深孔隔离注浆控制运营轨道变形施工技术,形成了一种隧道全断面注浆限制排水量保护既有线施工技术及既有线保护综合处理措施技术。

AN INDEFINITE-PROXIMAL-BASED STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD

The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requirements.He et al.(SIAM J.Optim.24:1011-1040,2014)proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a suitable underdetermined relaxation factor.In this paper,we further extend the so-called strictly contractive Peaceman-Rachford splitting method by using two different relaxation factors.Besides,motivated by the recent advances on the ADMM type method with indefinite proximal terms,we employ the indefinite proximal term in the strictly contractive Peaceman-Rachford splitting method.We show that the proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is convergent and also prove the o(1/t)convergence rate in the nonergodic sense.The numerical tests on the l 1 regularized least square problem demonstrate the efficiency of the proposed method.