CONVERGENCE_ANALYSIS

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Gradient-based algorithms for multi-objective bi-level optimization被引量：1
《Science China Mathematics》2024年第6期1419-1438,共20页Xinmin Yang Wei Yao Haian Yin Shangzhi Zeng Jin Zhang 
supported by the Major Program of National Natural Science Foundation of China(Grant Nos.11991020 and 11991024);supported by National Natural Science Foundation of China(Grant No.12371305);supported by National Natural Science Foundation of China(Grant No.12222106);Guangdong Basic and Applied Basic Research Foundation(Grant No.2022B1515020082);Shenzhen Science and Technology Program(Grant No.RCYX20200714114700072)。
Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably comple...
关键词：MULTI-OBJECTIVE bi-level optimization convergence analysis Pareto stationary learning to optimize 
The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid被引量：1
《Science China Mathematics》2024年第4期919-950,共32页Xiaoqing Chi Hui Zhang Xiaoyun Jiang 
supported by the Project of the National Key R&D Program(Grant No.2021YFA1000202);National Natural Science Foundation of China(Grant Nos.12120101001,12001326 and 12171283);Natural Science Foundation of Shandong Province(Grant Nos.ZR2021ZD03,ZR2020QA032 and ZR2019ZD42);China Postdoctoral Science Foundation(Grant Nos.BX20190191 and 2020M672038);the Startup Fund from Shandong University(Grant No.11140082063130)。
In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a h...
关键词：fractional MHD coupled flow and heat transfer model generalized second-grade fuid fast method convergence analysis numerical simulation 
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation
《Science China Mathematics》2024年第1期187-210,共24页Xiao Li Zhonghua Qiao Cheng Wang 
supported by the Chinese Academy of Sciences(CAS)Academy of Mathematics and Systems Science(AMSS);the Hong Kong Polytechnic University(PolyU)Joint Laboratory of Applied Mathematics;supported by the Hong Kong Research Council General Research Fund(Grant No.15300821);the Hong Kong Polytechnic University Grants(Grant Nos.1-BD8N,4-ZZMK and 1-ZVWW);supported by the Hong Kong Research Council Research Fellow Scheme(Grant No.RFS2021-5S03);General Research Fund(Grant No.15302919);supported by US National Science Foundation(Grant No.DMS-2012269)。
In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth ...
关键词：nonlocal Cahn-Hilliard equation second-order stabilized scheme higher-order consistency analysis rough and refined error estimate 
Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming
《Science China Mathematics》2022年第11期2397-2422,共26页Liang Chen Junyuan Zhu Xinyuan Zhao 
supported by National Natural Science Foundation of China (Grant No. 11801158);the Hunan Provincial Natural Science Foundation of China (Grant No. 2019JJ50040);the Fundamental Research Funds for the Central Universities in China;supported by National Natural Science Foundation of China (Grant No. 11871002);the General Program of Science and Technology of Beijing Municipal Education Commission (Grant No. KM201810005004)
In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.S...
关键词：second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming 
Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection被引量：4
《Science China Mathematics》2021年第5期887-902,共16页Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou 
supported by National Natural Science Foundation of China(Grant No.12071216);supported by National Natural Science Foundation of China(Grant No.11731006);the NNW2018-ZT4A06 project;supported by National Natural Science Foundation of China(Grant Nos.11822111,11688101 and 11731006);the Science Challenge Project(Grant No.TZ2018001)。
In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope selection.We firs...
关键词：molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis 
Convergence analysis of Oja’s iteration for solving online PCA with nonzero-mean samples被引量：2
《Science China Mathematics》2021年第4期849-868,共20页Siyun Zhou Yanqin Bai 
supported by National Natural Science Foundation of China(Grant No.11771275)。
Principal component analysis(PCA)is one of the most popular multivariate data analysis techniques for dimension reduction and data mining,and is widely used in many fields ranging from industry and biology to finance ...
关键词：online PCA Oja’s algorithm nonzero-mean samples convergence rate 
Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations被引量：1
《Science China Mathematics》2020年第1期39-60,共22页Mohammed Harunor Rashid Ya-xiang Yuan 
supported by CAS-President International Fellowship Initiative (PIFI), Chinese Academy of Sciences, Beijing, China;supported by National Natural Science Foundation of China (Grants Nos. 11688101 and 11331012)
Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:...
关键词：set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation 
Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs被引量：1
《Science China Mathematics》2017年第5期923-948,共26页LI Yang YANG Jie ZHAO WeiDong 
supported by Shanghai University Young Teacher Training Program(Grant No.slg14032);National Natural Science Foundations of China(Grant Nos.11501366 and 11571206)
In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson （C-N） scheme for solving decoupled FBSDEs. Based on the Taylor and ItS-Taylor expansions, the Malliavin calculus theory （...
关键词：convergence analysis Crank-Nicolson scheme decoupled forward backward stochastic differentialequations Malliavin calculus trapezoidal rule 
Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions
《Science China Mathematics》2016年第11期2245-2264,共20页MENG XiangYun YANG XueQin ZHANG Shuo 
supported by National Natural Science Foundation of China (Grant Nos. 11471026, 11271035, 91430213, 11421101 and 11101415)
We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of （D（h） order...
关键词：d-rectangular Morley element second order elliptic equation convergence analysis super convergence lower bound estimate 
Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems被引量：2
《Science China Mathematics》2016年第2期379-396,共18页ZHANG RuiLi TANG YiFa ZHU BeiBei TU XiongBiao ZHAO Yue 
supported by National Natural Science Foundation of China(Grant No.11371357);the Marine Public Welfare Project of China(Grant No.201105032)
Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in t...
关键词：convergence analysis formal energy symplectic method Hamiltonian system bushy tree 
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