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An alternating direction algorithm for matrix completion with nonnegative factors

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Frontiers of Mathematics in China 2012年第2期7卷 365-384页

作者： Yangyang XU wotao yin Zaiwen WEN yin ZHANG Department of Computational and Applied Mathematics Rice University Houston TX 77005 USA Department of Mathematics and Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known （to a certain accuracy）. This problem aggregates two existing problems：（i） nonnegative matrix factorization where all entries of M are given, and （ii） low-rank matrix completion where non- negativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on tile classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspeetral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.

关键词： nonnegative matrix factorization matrix completion alternating direction method hyperspectral unmixing

PROXIMAL-PROXIMAL-GRADIENT METHOD

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Journal of Computational Mathematics 2019年第6期37卷 778-812页

作者： Ernest K.Ryu wotao yin Department of Mathematics University of CaliforniaLos AngelesCA 90095USA

In this paper,we present the proximal-proximal-gradient method(PPG),a novel optimization method that is simple to implement and simple to *** generalizes the proximal-gradient method and ADMM and is applicable to minimization problems written as a sum of many differentiable and many non-differentiable convex *** non-differentiable functions can be *** furthermore present a related stochastic variation,which we call stochastic PPG(S-PPG).S-PPG can be interpreted as a generalization of Finito and MISO over to the sum of many coupled non-differentiable convex *** present many applications that can benefit from PPG and S-PPG and prove convergence for both *** demonstrate the empirical effectiveness of both methods through experiments on a CUDA GPU.A key strength of PPG and S-PPG is,compared to existing methods,their ability to directly handle a large sum of non-differentiable nonseparable functions with a constant stepsize independent of the number of *** non-diminishing stepsizes allows them to be fast.

关键词： Proximal-gradient ADMM Finito MISO SAGA Operator splitting Firstorder methods Distributed optimization Stochastic optimization Almost sure convergence linear convergence

On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

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Journal of the Operations Research Society of China 2019年第1期7卷 5-42页

作者： Zhimin Peng Yangyang Xu Ming Yan wotao yin Department of Mathematics University of CaliforniaLos AngelesCA 90095USA Department of Mathematical Sciences Rensselaer Polytechnic InstituteTroyNY 12180USA Department of ComputationalMathematics Science and Engineering Department of MathematicsMichigan State UniversityEast LansingMI 48824USA

Recent years have witnessed the surge of asynchronous parallel(asyncparallel)iterative algorithms due to problems involving very large-scale data and a large number of decision *** of asynchrony,the iterates are computed with outdated information,and the age of the outdated information,which we call delay,is the number of times it has been updated since its *** all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters ***,the maximum delay is practically *** paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint,and it allows for large unbounded *** explicit formula of stepsize that guarantees convergence is given depending on delays’*** p+1 identical processors,we empirically measured that delays closely follow the Poisson distribution with parameter p,matching our theoretical model,and thus,the stepsize can be set *** on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative,often slows down the convergence of the algorithm.

关键词： Asynchronous unbounded delays Nonconvex Convex

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无中心优化的算子分裂方法

计算数学 2019年第3期41卷 225-241页

作者：印卧涛阿里巴巴(美国)达摩院

在某些多智能体系统中,由于受到通讯等因素的限制,单个智能体只能进行本地计算,再与相邻智能体交换数据.与传统的并行和分布式计算不同,这种数据交换方式不再使用中心节点或者共享内存,而仅限于相邻节点之间.这种通过局部数据交换而实... 详细信息

在某些多智能体系统中,由于受到通讯等因素的限制,单个智能体只能进行本地计算,再与相邻智能体交换数据.与传统的并行和分布式计算不同,这种数据交换方式不再使用中心节点或者共享内存,而仅限于相邻节点之间.这种通过局部数据交换而实现全网目标的方式叫做无中心计算.比如,从任意的多个数开始,所有智能体通过不断地计算其局部平均,就都能收敛到这些数的平均值.无中心计算有不易形成通讯和计算瓶颈的优点,更适合分布的节点,因此受到一些应用的欢迎.本文介绍求解一致最优化问题的若干无中心算法.一致最优化问题的目标是全网所有节点的变量收敛到同一个、并使所有目标函数之和最小的值.我们可以通过推广求平均的无中心方法去实现这个目标,但是得到算法比普通(有中心的)优化算法收敛得更慢,有阶数差距.近年来,一些新的无中心算法弥补了这个阶数差距.本文采用算子分裂的统一框架,以比这些算法原文更为简单的形式介绍这些方法.

关键词：无中心算法一致优化算子分裂单调算子

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Preface

Communications on Applied Mathematics and Computation 2024年第2期6卷 1-2页

作者： Qing Nie Chi-Wang Shu Yulong Xing Yong-Tao Zhang University of California Irvine IrvineCAUSA Brown University ProvidenceRIUSA The Ohio State University ColumbusOHUSA University of Notre Dame Notre DameINUSA

This focused issue of the Communications on Applied Mathematics and Computation is dedicated to the memory of Professor Ching-Shan Chou,who passed away in November *** her passing,our community of applied mathematicia... 详细信息

关键词： passing brilliant passed

Correction to:On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

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Journal of the Operations Research Society of China 2023年第4期11卷 977-977页

作者： Peng, Zhimin Xu, Yangyang Yan, Ming yin, wotao Department of Mathematics University of California Los Angeles USA Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy USA Department of Computational Mathematics Science and Engineering Department of Mathematics Michigan State University East Lansing USA

The article “On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays”, written by Zhimin Peng, Yangyang Xu, Ming Yan, wotao yin was originally published electronically on the publisher’s Interne...

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Hydrogen and nitrogen absorption properties of Ce-added Zr_(2)(Fe_(1-x)Ni_(x)) alloys

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Journal of Rare Earths 2024年第6期42卷 1136-1141,I0005页

作者： Kai yin Xiaopeng Liu State Key Laboratory of Advanced Materials for Smart Sensing GRINM Group Co.Ltd.Beijing10088China GRIMAT Engineering Institute Co. Ltd.Beijing101407China General Research Institute of Nonferrous Metals Beijing100088China

To improve the nitriding resistance of Zr_(2)Fe alloy,the Ce-added Zr_(2)(Fe_(1-x)Ni_(x))(x=0,0.15,0.3,0.5)alloys were prepared by magnetic levitation melting *** effects of Ni substitution for Fe on the phase structure,hydrogen and nitrogen absorption properties of the alloys were investigated by X-ray diffraction,scanning electron microscopy and p-c isotherm *** experimental results show that Ni substitution can effectively inhibit the formation of both α-Zr and ZrFe_(2) phases and promote the formation of C16 structure Zr_(2)(Fe,Ni)phase,causing Ni-substituted alloys to exhibit low nitrogen absorption rate and *** 623 K under 0.5 MPa nitrogen pressure,the nitrogen absorption capacity of Ce-added Zr_(2)(Fe_(0.5)Ni_(0.5))alloy reaches to 0.8 mL/g,much lower than that of Zr_(2)Fe alloy(1.5 mL/g).Ni substitution decreases the crystal cell volume of the C_(16)Zr_(2)(Fe,Ni)phase,resulting in an increase in the hydrogen absorption equilibrium *** 623 K under 0.05 MPa hydrogen pressure,the hydrogen absorption capacity decreases from 1.46 wt%of Zr_(2)Fe alloy to 1.41 wt%of Ce-added Zr_(2)(Fe_(0.5)Ni_(0.5))alloy.

关键词： Zr_(2)Fe alloy Ce Pressure-composition isotherm Hydrogen absorption Nitrogen absorption Rare earths

Rational surface charge engineering of haloalkane dehalogenase for boosting the enzymatic performance in organic solvent solutions

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Chinese Journal of Chemical Engineering 2024年第1期65卷 276-285页

作者： yin Wu Yan Sun Department of Biochemical Engineering School of Chemical Engineering and Technology and Key Laboratory of Systems Bioengineering and Frontiers Science Center for Synthetic Biology(Ministry of Education)Tianjin UniversityTianjin 300350China

Biocatalysis in organic solvents(OSs)has numerous important applications,but native enzymes in OSs often exhibit limited catalytic ***,we proposed a computation-aided surface charge engineering strategy to improve the catalytic performance of haloalkane dehalogenase DhaA in OSs based on the energetic analysis of substrate binding to the DhaA *** variants with enhanced OS resistance were obtained by replacing negative charged residues on the surface with positive charged residue(Arg).Particularly,a four-substitution variant E16R/E93R/E121R/E257R exhibited the best catalytic performance(five-fold improvement in OS resistance and seven-fold half-life increase in 40%(vol)dimethylsulfoxide).As a result,the overall catalytic performance of the variant could be at least 26 times higher than the wild-type *** spectroscopy and molecular dynamics simulation studies revealed that the residue substitution mainly enhanced OS resistance from four aspects:(a)improved the overall structural stability,(b)increased the hydrophobicity of the local microenvironment around the catalytic triad,(c)enriched the hydrophobic substrate around the enzyme molecule,and(d)lowered the contact frequency between OS molecules and the catalytic *** findings validate that computationaided surface charge engineering is an effective and ingenious rational strategy for tailoring enzyme performance in OSs.

关键词： Surface charge engineering Organic solvent resistance Molecular dynamics simulation Haloalkane dehalogenase

A generalized presentation of multi-caloric effects based on exterior derivative theory and its applications

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Communications in Theoretical Physics 2024年第8期76卷 156-163页

作者： Jun yin School of Materials Science and Engineering Nankai UniversityTianjin 300350China School of Mechanical Engineering and Automation Fuzhou UniversityFuzhou 350108China

The emerging concept of multi-caloric effects, introduced in 2010, entails the application of multiple interplay fields to a thermodynamic system. While multi-caloric effects are the main focus of experimental endeavors, theoretical considerations fall short of providing a thorough understanding. This paper introduces a comprehensive presentation on multi-caloric effects,employing the method and theory of exterior derivative formations. It addresses every aspect of thermodynamic systems, showcasing its applicability to multi-caloric materials(both singlephase and multi-phase materials), and its adaptability to different scenarios(either in single or multiple force fields). The formulation of Maxwell relationships, characterized by their generality and universality, enables a clear prediction in entropy and temperature, facilitating a distinct identification between independent and interdependent contributions from multi-caloric effects. These insights hold significant importance in designing and developing specialized thermodynamic materials, optimizing functional performances and exploring innovative mechanisms.

关键词： multicaloric effects Maxwell relations isothermal entropy adiabatic temperature