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Optimality Conditions for Rank-Constrained Matrix Optimization

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Journal of the Operations Research Society of China 2019年第2期7卷 285-301页

作者： Xin-Rong Li Wen Song nai-hua xiu Department of Applied Mathematics Beijing Jiaotong UniversityBeijing 100044China School of Mathematical Sciences Harbin Normal UniversityHarbin 150025China

In this paper,we comprehensively study optimality conditions for rank-constrained matrix optimization(RCMO).By calculating the Clarke tangent and normal cones to a rank-constrained set,along with the given Fréchet,Mordukhovich normal cones,we investigate four kinds of stationary points of the RCMO and analyze the relations between each stationary point and local/global minimizer of the ***,the second-order optimality condition of the RCMO is achieved with the help of the Clarke tangent cone.

关键词： Matrix optimization Rank constraint Normal cone First-order optimality condition Second-order optimality condition

Preface:Special Issue on Data-Driven Optimization Models and Algorithms

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Journal of the Operations Research Society of China 2015年第4期3卷 389-390页

作者： Yan-Qin Bai Yu-Hong Dai nai-hua xiu Shanghai University Shanghai 200444China Chinese Academy of Sciences Beijing 100190China Beijing Jiaotong University Beijing 100044China

The growing demands of information age have speeded up the development of data *** research and application of data become more and more popular in many fields,such as information science,mathematics,operations research,statistics and computer *** is of theoretical significance to study the optimization models and algorithms driven by data,which is helpful to new business model,communication and network technology,intelligent transportation system,economic management and other related fields.

关键词： computer operations network

Simultaneous Approximation of Multi-criteria Submodular Function Maximization

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Journal of the Operations Research Society of China 2014年第3期2卷 271-290页

作者： Dong-Lei Du Yu Li nai-hua xiu Da-Chuan Xu Faculty of Business Administration University of New BrunswickFrederictonNB E3B 9Y2Canada Department of Mathematics School of ScienceBeijing Jiaotong University3 ShangyuancunHaidian DistrictBeijing 100044China Department of Applied Mathematics Beijing University of Technology100 PingleyuanChaoyang DistrictBeijing 100124China

Recently intensive interest has been raised on approximation of the NPhard submodular maximization problem due to their theoretical and practical *** this work,we extend this line of research by focusing on the simultaneous approximation of multiple submodular function *** address the existence and nonexistence results for both deterministic and randomized approximation when the submodular functions are symmetric and asymmetric,respectively,along with algorithmic *** offer complete characterization of the symmetric case and partial results on the asymmetric case.

关键词： Multi-criteria Submodular function maximization Approximation algorithm Existence

Sparse and Low-Rank Covariance Matrix Estimation

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Journal of the Operations Research Society of China 2015年第2期3卷 231-250页

作者： Sheng-Long Zhou nai-hua xiu Zi-Yan Luo Ling-Chen Kong Department of Applied Mathematics Beijing Jiaotong UniversityBeijing 100044China State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong UniversityBeijing 100044China

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance *** first benefit from a convex optimization which develops l1-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank *** the proposed estimator,we then prove that with high probability,the Frobenius norm of the estimation rate can be of order O(√((slgg p)/n))under a mild case,where s and p denote the number of nonzero entries and the dimension of the population covariance,respectively and n notes the sample ***,an efficient alternating direction method of multipliers with global convergence is proposed to tackle this problem,and merits of the approach are also illustrated by practicing numerical simulations.

关键词： Covariance matrix Sparse and low-rank estimator Estimation rate Alternating direction method of multipliers

ON THE LINEAR CONVERGENCE OF PC-METHOD FOR ACLASS OF LINEAR VARIATIONAL INEQUALITIES

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Journal of Computational Mathematics 1999年第2期17卷 199-208页

作者： nai-hua xiu(Department of Mathematics, Nothern Jiaotong University, Beijing 100044, China Instituteof Applied Mathematics, Chinese Academy Of Sciences, Beijing 100080, China) 北方交通大学数学系北京

This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Metho... 详细信息

关键词： affine variational inequality projection and contraction method linear convergence

Machine learning for prediction of retained austenite fraction and optimization of processing in quenched and partitioned steels

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Journal of Iron and Steel Research International 2024年第8期31卷 2002-2013页

作者： Shuai Wang Jie Li Li-yang Zeng Xun-wei Zuo nai-lu Chen Yong-hua Rongg Shanghai Key Laboratory of Materials Laser Processing and Modification School of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghai 200240China School of Materials Science and Engineering Shanghai Jiao Tong UniversityShanghai 200240China

The metastable retained austenite(RA)plays a significant role in the excellent mechanical performance of quenching and partitioning(Q&P)steels,while the volume fraction of RA(V_(RA))is challengeable to directly predict due to the complicated relationships between the chemical composition and process(like quenching temperature(Qr)).A Gaussian process regression model in machine learning was developed to predict V_(RA),and the model accuracy was further improved by introducing a metallurgical parameter of martensite fraction(fo)to accurately predict V_(RA) in Q&P *** developed machine learning model combined with Bayesian global optimization can serve as another selection strategy for the quenching temperature,and this strategy is very effcient as it found the"optimum"Qr with the maximum V_(RA) using only seven consecutive *** benchmark experiment also reveals that the developed machine learning model predicts V_(RA) more accurately than the popular constrained carbon equilibrium thermodynamic model,even better than a thermo-kinetic quenching-partitioning-tempering-local equilibrium model.

关键词： Q&P steel Retained austenite fraction Machine learning Quenching temperature Gaussian process regression model

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几类非线性问题解的通有唯一性

数学学报（中文版） 2014年第2期57卷 373-386页

作者：彭定涛俞建修乃华贵州大学理学院贵阳550025 北京交通大学理学院北京100044

首先给出集值映射的几个通有唯一性定理,然后将其应用于研究极大极小问题、向量优化问题和不动点问题等解的唯一性.证明了在Baire分类意义下,大多数极大极小问题、向量优化问题和不动点问题都有唯一解.

关键词：通有唯一性集值映射极大极小问题向量优化问题不动点问题

The coupling control of biological precursors and environmental factors onβ-carotane enrichment in alkaline lacustrine source rocks:A case study from the Fengcheng formation in the western Junggar Basin,NW China

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Petroleum Science 2024年第2期21卷 836-854页

作者： Mao-Guo Hou Ming Zha hua Liu Hai-Lei Liu Jiang-xiu Qu Ablimit Imin xiu-Jian Ding Zhong-Fa Jiang School of Geosciences China University of PetroleumQingdaoShandong266580China Research Institute of Exploration and Development Xinjiang Petroleum Administration BureauKaramayXinjiang834000China

The organic-rich mudstones and dolostones of the Permian Fengcheng Formation(Fm.)are typically alkaline lacustrine source rocks,which are typified by impressively abundantβ-*** β-carotane has been well acknowledged as an effective indicator of biological sources or depositional ***,the specific biological sources of β-carotane and the coupling control of biological sources and environmental factors on the enrichment of β-carotane in the Fengcheng *** *** on a comprehensive investigation of the bulk,molecular geochemistry,and organic petrology of sedimentary rocks and the biochemistry of phytoplankton in modern alkaline lakes,we proposed a new understanding of the biological precursors of β-carotane and elucidated the enrichment mechanism of β-carotane in the Fengcheng *** results show that the biological precursors crucially control the enrichment of β-carotane in the Fengcheng *** haloalkaliphilic cyanobacteria are the primary biological sources of β-carotane,which is suggested by a good positive correlation between the 2-methylhopane index,7-+8-methyl heptadecanes/C_(max),C_(29%),and β-carotane/C_(max)in sedimentary rocks and the predominance of cyanobacteria with abundantβ-carotene in modern alkaline *** enrichment of β-carotane requires the reducing condition,and the paleoredox state that affects the enrichment of β-carotane appears to have a *** paleoclimate conditions do not considerably impact the enrichment of β-carotane,but they have some influence on the water's paleosalinity by affecting evaporation and *** it does not directly affect the enrichment of β-carotane in the Fengcheng Fm.,paleosalinity does have an impact on the cyanobacterial precursor supply and the preservation conditions.

关键词： β-carotane enrichment Cyanobacterial input Environmental impact Alkaline lacustrine source rocks The Fengcheng formation

Central environmental protection inspection and carbon emission reduction: A tripartite evolutionary game model from the perspective of carbon neutrality

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Petroleum Science 2024年第3期21卷 2139-2153页

作者： Zhen-hua Zhang Dan Ling Qin-Xin Yang Yan-Chao Feng Jing xiu School of Economics Lanzhou UniversityLanzhou 730000GansuChina Institute of Green Finance Lanzhou UniversityLanzhou 730000GansuChina School of Management Lanzhou UniversityLanzhou 730000GansuChina School of Business Zhengzhou UniversityZhengzhou 450001HenanChina Institute of Economics Jilin Academy of Social SciencesChangchun130033JilinChina

Since the carbon neutrality target was proposed,many countries have been facing severe challenges to carbon emission reduction *** study is conducted using a tripartite evolutionary game model to explore the impact of the central environmental protection inspection(CEPI)on driving carbon emission reduction,and to study what factors influence the strategic choices of each party and how they interact with each *** research results suggest that local governments and manufacturing enterprises would choose strategies that are beneficial to carbon reduction when CEPI *** the initial willingness of all parties increases 20%,50%—80%,the time spent for the whole system to achieve stability decreases from 100%,60%—30%.The evolutionary result of“thorough inspection,regulation implementation,low-carbon management”is the best strategy for the tripartite evolutionary ***,the smaller the cost and the larger the benefit,the greater the likelihood of the three-party game stability strategy *** study has important guiding significance for other developing countries to promote carbon emission reduction by environmental policy.

关键词： Central environmental protection inspection Local government Manufacturing enterprise Tripartite evolutionary game Carbon emission reduction