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EXTENDED LEVENBERG-MARQUARDT METHOD FOR composite function MINIMIZATION

Journal of Computational Mathematics 2017年第4期35卷 529-546页

作者： Jianchao Huang Zaiwen Wen Xiantao Xiao School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240 China Beijing International Center for Mathematical Research Peking University Beijing 100871 China School of Mathematical Sciences Dalian University of Technology Dalian 116024 China

In this paper, we propose an extended Levenberg-Marquardt （ELM） framework that generalizes the classic Levenberg-Marquardt （LM） method to solve the unconstrained minimization problem min ρ（r（x））, where r ： Rn→ Rm and ρ ： Rm → R. We also develop a few inexact variants which generalize ELM to the cases where the inner subproblem is not solved exactly and the Jaeobian is simplified, or perturbed. Global convergence and local superlinear convergence are established under certain suitable conditions. Numerical results show that our methods are promising.

关键词： Unconstrained minimization composite function Levenberg-Marquardt method.

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ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF composite functionAL EQUATIONS

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Acta Mathematica Scientia 2012年第2期32卷 800-806页

作者：高凌云 Department of Mathematics Jinan University

In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning ... 详细信息

关键词： meromorphic solution composite function functional equations

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ON MATRIX AND DETERMINANT IDENTITIES FOR composite functionS

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Journal of Computational Mathematics 2011年第1期29卷 16-25页

作者： XinghuaWang Aimin Xu Department of Mathematics Zhejiang University Hangzhou 310027 China Institute of Mathematics Zhejiang Wdnli University Ningbo 315100 China

We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can b... 详细信息

关键词： Bell polynomial composite function Determinant identity Divided difference,Matrix identity.

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Multi-objective constructal design for quadrilateral heat generation body based on thermal-entransy theory and NSGA-Ⅱ

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Science China(Technological Sciences) 2024年第9期67卷 2777-2786页

作者： CHEN LinGen ZHU HongWei GE YanLin SHI ShuangShuang FENG HuiJun Institute of Thermal Science and Power Engineering Wuhan Institute of TechnologyWuhan 430205China Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment Wuhan 430205China School of Mechanical Electrical EngineeringWuhan Institute of TechnologyWuhan 430205China

Based on thermal-entransy theory, the multi-objective constructal design of quadrilateral heat generation body(HGB) with similar shapes of leaves is studied further. The relationship between the aspect ratio of quadrilateral HGB and average temperature difference based on thermal-entransy dissipation is compared with that between the aspect ratio of quadrilateral HGB and the maximum temperature difference(MTD). The relationship between a composite function, consisting of linear weighting sum of the average temperature difference and MTD, and aspect ratio is obtained, and the optimal aspect ratios under minimum composite function with different weighting coefficients are obtained. Using the NSGA-Ⅱ algorithm, the Pareto frontier containing a series of compromise results of average temperature difference and MTD is obtained, and optimization results are compared using the deviation index. There is no aspect ratio to make both MTD and average temperature difference reach the minimum, and the optimal aspect ratio under the minimum MTD is smaller than that under the minimum average temperature difference. The optimal aspect ratio is obtained by making the composite function reach the minimum, and the optimal aspect ratios obtained by minimizing the composite function with different weighting coefficients are different. Compared with the construct of the initial design, the value of the composite function with optimal construct decreases by 1.9%, and the aspect ratio of the quadrilateral HGB decreases by 9.1%. The average temperature difference with the optimal construct increases by 2.1%, and the MTD with the optimal construct decreases by 5.6%. The deviation index under multi-objective optimization is smaller than that under single-objective optimization, and the obtained construct has better comprehensive thermal conductivity. Compared with TOPSIS and LINMAP decision-making methods, the average temperature difference with composite function optimization increases by 0.5

关键词： thermal-entransy theory constructal theory heat conduction quadrilateral heat generation body composite function NSGA-Ⅱ

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ON THE DIVIDED DIFFERENCE FORM OF FAA DI BRUNO＇S FORMULA

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Journal of Computational Mathematics 2006年第4期24卷 553-560页

作者： Xing-hua Wang He-yu Wang Department of Mathematics Zhejiang University Hangzhou 310028 China Computer Science School Zhejiang University Hangzhou 310027 China Mathematics Department of Hong Kong Baptist University Kowloon Hong Kong

The n-divided difference of the composite function h ：= f o g of functions f, g at a group of nodes t0,t1,…,tn is shown by the combinations of divided differences of f at the group of nodes g（t0）,g（t1）,…,g（tm） and divided differences of g at several partial group of nodes t0,t1,…,tn, where m = 1,2,…,n. Especially, when the given group of nodes are equal to each other completely, it will lead to Faà di Bruno＇s formula of higher derivatives of function h.

关键词： Divided difference Newton interpolation composite function FAA di Bruno's formula Bell polynomial

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