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Superlinear Convergence of Affine Scaling Interior Point Newton Method for Linear Inequality Constrained Minimization without Strict Complementarity

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 183-194页

作者： de-tong zhu Business College Shanghai Normal University Shanghai 200234 China

In this paper we extend and improve the classical affine scaling interior-point Newton method for solving nonlinear optimization subject to linear inequality constraints in the absence of the strict complementarity assumption. Introducing a computationally efficient technique and employing an identification function for the definition of the new affine scaling matrix, we propose and analyze a new affine scaling interior-point Newton method which improves the Coleman and Li affine sealing matrix in [2] for solving the linear inequlity constrained optimization. Local superlinear and quadratical convergence of the proposed algorithm is established under the strong second order sufficiency condition without assuming strict complementarity of the solution.

关键词： Interior method affine scaling strict complementarity

Global and Local Convergence of a New Affine Scaling Trust Region Algorithm for Linearly Constrained Optimization

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Acta Mathematica Sinica,English Series 2016年第10期32卷 1203-1213页

作者： Chao GU de tong zhu School of Mathematics and Information Shanghai LiXin University of Commerce department of Mathematics Shanghai Normal University

Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.

关键词： Linearly constrained optimization affine scaling trust region dwindling filter~ conver-gence

On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1804-1828页

作者： Yong Gang PEI de tong zhu Mathematics and Information Science He 'nan Normal University Xinxiang 453007 P. R. China Mathematics and Science College Shanghai Normal University Shanghai 200234 P. R. China

A trust-region sequential quadratic programming （SQP） method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the trans- position of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported.

关键词： Sequential quadratic programming trust-region filter line search projection global convergence

A Filter Line Search Algorithm Based on an Inexact Newton Method for Nonconvex Equality Constrained Optimization

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 687-698页

作者： zhu-jun WANG de-tong zhu Cun-yun NIE College of Science Hunan Institute of Engineering College of Mathematics and Science Shanghai Normal University

We propose an inexact Newton method with a filter line search algorithm for nonconvex equality constrained optimization. Inexact Newton＇s methods are needed for large-scale applications which the iteration matrix cannot be explicitly formed or factored. We incorporate inexact Newton strategies in filter line search, yielding algorithm that can ensure global convergence. An analysis of the global behavior of the algorithm and numerical results on a collection of test problems are presented.

关键词： nonconvex constrained optimization filter line search inexact Newton method

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 2001年第3期19卷 241-258页

作者： de-tong zhu (department of Mathematics, Shanghai Normal University, Shanghai 200234, China) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

A Nonmonotone Hybrid Method of Conjugate Gradient and Lanczos-type for Solving Nonlinear Systems

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Journal of the Operations Research Society of China 2014年第3期2卷 291-305页

作者： Chun-Xia Jia Jue-Yu Wang de-tong zhu department of Mathematics Shanghai Normal UniversityShanghai 200234China department of Mathematics Shanghai Normal UniversityGuilin Road 100Shanghai 200234China

In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear *** iterative direction can be obtained by solving a quadratic model via conjugate gradient and Lanczos *** the backtracking line search,we will find an acceptable trial step size along this direction which makes the objective function nonmonotonically decreasing and makes the norm of the step size monotonically *** convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable ***,we present some numerical results to illustrate the effectiveness of the proposed algorithm.

关键词： Nonmonotonic technique Nonlinear systems Lanczos method Conjugate gradient

一种非单调滤子信赖域算法解线性不等式约束优化

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数学学报（中文版） 2020年第6期63卷 601-620页

作者：王珏钰顾超朱德通上海立信会计金融学院统计与数学学院上海201209 上海师范大学数学系上海200234

本文给出了一种新的多维滤子算法结合非单调信赖域策略解线性约束优化.目标函数及其投影梯度的分量组成了新的多维滤子,并且与信赖域半径有关.当信赖域半径充分小时,新的滤子能接受试探点,避免算法无限循环.非单调信赖域策略保证了新算... 详细信息

本文给出了一种新的多维滤子算法结合非单调信赖域策略解线性约束优化.目标函数及其投影梯度的分量组成了新的多维滤子,并且与信赖域半径有关.当信赖域半径充分小时,新的滤子能接受试探点,避免算法无限循环.非单调信赖域策略保证了新算法的整体收敛性.目前为止,多维滤子算法局部收敛性分析仍然没有解决,在合理假设下,我们分析了新算法的局部超线性收敛性.数值结果验证了算法的有效性.

关键词：线性不等式约束优化多维滤子非单调信赖域策略局部收敛性

一种解非线性方程组的不精确牛顿——兰索斯方法

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数学学报（中文版） 2023年第2期66卷 317-338页

作者：顾超王珏钰朱德通上海立信会计金融学院统计与数学学院上海201209 上海师范大学数学系上海200234

本文提出一种不完全线搜索技术的不精确牛顿—克雷洛夫(Newton-Krylov)子空间方法解对称非线性方程组,其中克雷洛夫子空间方法采用的是兰索斯(Lanczos)类分解技术.迭代方向是通过使用兰索斯方法近似求解非线性方程组的牛顿方程获得的.... 详细信息

本文提出一种不完全线搜索技术的不精确牛顿—克雷洛夫(Newton-Krylov)子空间方法解对称非线性方程组,其中克雷洛夫子空间方法采用的是兰索斯(Lanczos)类分解技术.迭代方向是通过使用兰索斯方法近似求解非线性方程组的牛顿方程获得的.在合理的假设条件下,分析了算法的全局收敛性和局部超线性收敛速率.最后,数值结果显示了该算法的有效性.

关键词：不精确牛顿法牛顿—克雷洛夫子空间方法全局收敛性兰索斯方法对称非线性方程组

Effects of Bifidobacterium lactis BLa80 on fecal and mucosal flora and stem cell factor/c-kit signaling pathway in simulated microgravity rats

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World Journal of Gastroenterology 2025年第1期31卷 93-109页

作者： Ping Zhang Ying zhu Pu Chen tong Zhou Zhe-Yi Han Jun Xiao Jian-Feng Ma Wen Ma Peng Zang Ying Chen Graduate School Hebei North UniversityZhangjiakou 075000Hebei ProvinceChina Key Laboratory of Aerospace Nutrition and Food Engineering China Astronaut Research and Training CenterBeijing 100094China department of Gastroenterology The Air Force Medical CenterBeijing 100142China department of Blood Transfusion Air Force Medical CenterBeijing 100142China

BACKGROUND Simulated microgravity environment can lead to gastrointestinal motility *** pathogenesis of gastrointestinal motility disorders is closely related to the stem cell factor(SCF)/c-kit signaling pathway associated with intestinal flora and Cajal stromal ***,intestinal flora can also affect the regulation of SCF/c-kit signaling pathway,thus affecting the expression of Cajal stromal *** cells are the pacemakers of gastrointestinal *** To investigate the effects of Bifidobacterium lactis(***)BLa80 on the intestinal flora of rats in simulated microgravity and on the gastrointestinal motility-related SCF/c-kit *** The internationally recognized tail suspension animal model was used to simulate the microgravity environment,and 30 rats were randomly divided into control group,tail suspension group and drug administration tail suspension group with 10 rats in each group for a total of 28 *** tail group was given *** BLa80 by intragastric administration,and the other two groups were given water intragastric administration,the concentration of intragastric administration was 0.1 g/mL,and each rat was 1 mL/***&eosin staining was used to observe the histopathological changes in each segment of the intestine of each group,and the expression levels of SCF,c-kit,extracellular signal-regulated kinase(ERK)and p-ERK in the gastric antrum of each group were detected by Western blotting and *** fecal flora and mucosal flora of rats in each group were detected by 16S *** Simulated microgravity resulted in severe exfoliation of villi of duodenum,jejunum and ileum in rats,marked damage,increased space between villi,loose arrangement,shortened columnar epithelium of colon,less folds,narrower mucosal thickness,reduced goblet cell number and crypts,and significant improvement after probiotic *** microgravity reduced the expressions of SCF and c-kit,and increased the express

关键词： Simulated microgravity Rat Intestinal flora Gastrointestinal motility Stem cell factor/c-kit signaling pathway