Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.     

The single-polarization filter composed of gold-coated photonic crystal fiber

A single-polarization filter comprising a gold-coated photonic crystal fiber based on surface plasmon resonance is designed and investigated. The pattern matching and coupled polarization characteristics analyzed by the full-vector finite element method (FEM) and losses at 1,540 nm are achieved to 1,016.01739 dB/cm (x-pol core mode) and 33.81917 dB/cm (y-pol core mode). The crosstalk (CT) value of the 1,540 nm band is ?853.12653 dB for fiber length $L=1,000\mathrm{\mu }\text{m}$ and the bandwidth is 850 nm. The working wavelength of the filter ranges from 1,280 nm to 1,540 nm by varying the diameter of outer air holes ($d_1$), the diameter of inner air holes ($d_4$), the metal film thickness (t), as well as the liquid refractive index (n).     

介质加载环板慢波结构高频特性研究

 提出了一种适用于环板结构的计算等效相对介电常数的方法，利用变分法导出了介质加载环板慢波结构的色散方程和耦合阻抗表达式。计算结果表明，介质加载能够有效降低环板慢波结构的工作电压。计算结果与CST-MWS的模拟结果吻合良好，说明所提出的计算等效相对介电常数的方法和计算色散方程的方法对环板慢波结构是切实可行的。     

锐钛矿二氧化钛超细纳米晶的三声子互作用

本文通过对粒径为2.2-25.5nm的锐钛矿二氧化钛超细纳米晶在83-293 K温度范围内的变温拉曼光谱的研究,得到了三声子互作用对拉曼频率和线宽的贡献随粒径的变化关系。结果表明锐钛矿二氧化钛超细纳米晶的三声子相互作用随粒径减小而加强。     

光子晶体在座舱罩雷达散射截面减缩中的应用

提出一种金属 介质型光子晶体薄膜，用传输矩阵法计算这种光子晶体薄膜的反射率和透射率。计算结果表明，这种光子晶体薄膜对毫米和厘米量级的微波的反射率高达99％以上；对于波长为微米量级的可见光，平均透光率为50％。分析了介质单元厚度、金属单元厚度、金属层总厚度对透射率的影响，给出这种光子晶体薄膜的材料选择和结构设计应遵循的原则。指出这种光子晶体薄膜涂镀在飞机座舱玻璃上，可以有效地减小座舱罩的雷达散射截面。     

纳米颗粒团聚物流化特性的数值研究

基于气固两相流体动力学理论,建立气体纳米颗粒团聚物两相流动双流体模型.模型中采用了Jung ＆ Gidaspow (2002)测量的固相应力模量和王垚等(2001)提出的聚团曳力系数计算模型.对纳米颗粒团聚物的流化过程进行了数值模拟,得到纳米颗粒团聚物的流化特性.模拟得出的床层膨胀比与文献中实验的结果较为接近.     

高温超导体Josephson阵列在磁场中的微波响应与磁通涡旋激发

本文从分析相变电阻率 ρP 和磁通蠕动电阻率 ρF 出发 ,指出当T小于某一温度T0 时 ,ρF>ρP,而当T >T0 时 ,ρF 远小于 ρP,并进一步分析了 ρF 与 ρP 随温度的变化率分布图 ,得出磁通蠕动电阻率 ρF 随温度的变化率分布图跟微波响应曲线具有相似的分布特征 ,结果表明 :高温超导体的非平衡微波响应机制可能与磁通涡旋的激发有关 .     

螺旋线径向挤压变形对其慢波结构冷测特性的影响

 介绍了用MAFIA软件的准周期边界条件计算螺旋线行波管慢波结构的色散和耦合阻抗，以及用ANSYS软件对螺旋线径向挤压变形建模的方法，并对螺旋线受挤压径向变形对其冷测特性的影响进行了详细的分析。结果表明:螺旋线径向挤压变形会导致相速增大，而在通常的变形范围内耦合阻抗也会增加；当变形继续增大时耦合阻抗上升到最大值后开始下降。     

基于成像机理的小波包变换多聚焦图像融合

由于可见光成像系统的聚焦范围有限,因而在成像过程中,除聚焦良好的物体能生成清晰的图像外,该物体前后一定距离外的所有物体都将呈现不同程度的模糊.为了获得场景内所有物体均清晰的图像,在分析了多聚焦图像成像机理的基础上,提出了一种基于小波包变换的融合方法.它是将成像系统先聚焦在一部分对象上,得到其清晰的图像;然后再将其聚焦在另一部分对象上,得到另一清晰的图像;最后把这两幅实验图像加以融合,从而获得场景内所有物体均清晰的图像.实验结果表明,基于小波包变换的融合方法能够将信号的频带进行多层次划分,对高频成分也能进一步地分解,可有效综合多聚焦图像.