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A Modified Three-Term Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization

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Computers, Materials & Continua 2020年第2期62卷 787-800页

作者： Wujie Hu gonglin yuan Hongtruong Pham College of Mathematics and Information Science Guangxi UniversityNanningChina Thai Nguyen University of Economics and Business Administration Thai NguyenVietnam

It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth *** perfect algorithm stems from concept of‘bundle’successfully addresses both smooth and nonsmooth complex problems,but it is regrettable that it is merely effective to small and medium optimization models since it needs to store and update relevant information of parameter’s *** conjugate gradient algorithm is effective both large-scale smooth and nonsmooth optimization model since its simplicity that utilizes objective function’s information and the technique of Moreau-Yosida ***,a modified three-term conjugate gradient algorithm was proposed,and it has a sufficiently descent property and a trust region *** the same time,it possesses the global convergence under mild assumptions and numerical test proves it is efficient than similar optimization algorithms.

关键词： Conjugate gradient large-scale trust region global convergence

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

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Acta Mathematica Scientia 2024年第5期44卷 1735-1746页

作者： gonglin yuan Xiong ZHAO Jiajia YU School of Mathematics and Information Science Center for Applied Mathematics of Guangxi(Guangxi University)Guangxi UniversityNanning530004China

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization *** global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS *** some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection ***,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

关键词： cautious BFGS nonconvex problems Lipschitz continuity projection technique global convergence

An Active-Set Projected Trust Region Algorithm for Box Constrained Optimization Problems

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1128-1147页

作者： yuan gonglin WEI Zengxin ZHANG Maojun College of Mathematics and Information Science Guangxi University School of Mathematic and Computing Science Guilin University of Electronic Technology

关键词： Active-set strategy convergence trust region

A Nonmonotone Line Search Method for Symmetric Nonlinear Equations

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Intelligent Control and Automation 2010年第1期1卷 28-35页

作者： gonglin yuan Laisheng Yu 不详

In this paper, we propose a new method which based on the nonmonotone line search technique for solving symmetric nonlinear equations. The method can ensure that the search direction is descent for the norm function. Under suitable conditions, the global convergence of the method is proved. Numerical results show that the presented method is practicable for the test problems.

关键词： Nonmonotone Line Search Symmetric Equations Global Convergence

A Line Search Algorithm for Unconstrained Optimization

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Journal of Software Engineering and Applications 2010年第5期3卷 503-509页

作者： gonglin yuan Sha Lu Zengxin Wei College of Mathematics and Information Science Guangxi University Nanning China School of Mathematical Science Guangxi Teachers Education University Nanning China.

It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.

关键词： Line Search Unconstrained Optimization Global Convergence R-linear Convergence

A Modified Limited SQP Method For Constrained Optimization

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Applied Mathematics 2010年第1期1卷 8-17页

作者： gonglin yuan Sha Lu Zhengxin Wei Department of Mathematics and Information Science Guangxi University Nanning China School of Mathematics Science Guangxi Teacher’s Education University Nanning China

In this paper, a modified variation of the Limited SQP method is presented for constrained optimization. This method possesses not only the information of gradient but also the information of function value. Moreover, the proposed method requires no more function or derivative evaluations and hardly more storage or arithmetic operations. Under suitable conditions, the global convergence is established.

关键词： Constrained Optimization Limited Method SQP Method Global Convergence

On the Global Convergence of the PERRY-SHANNO Method for Nonconvex Unconstrained Optimization Problems

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Applied Mathematics 2011年第3期2卷 315-320页

作者： Linghua Huang Qingjun Wu gonglin yuan 不详

In this paper, we prove the global convergence of the Perry-Shanno’s memoryless quasi-Newton (PSMQN) method with a new inexact line search when applied to nonconvex unconstrained minimization problems. Preliminary nu... 详细信息

关键词： Unconstrained Optimization Nonconvex Optimization Global Convergence

A Rank-One Fitting Method with Descent Direction for Solving Symmetric Nonlinear Equations

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International Journal of Communications, Network and System Sciences 2009年第6期2卷 555-561页

作者： gonglin yuan Zhongxing WANG Zengxin WEI 不详

In this paper, a rank-one updated method for solving symmetric nonlinear equations is proposed. This method possesses some features: 1) The updated matrix is positive definite whatever line search technique is used;2) The search direction is descent for the norm function;3) The global convergence of the given method is established under reasonable conditions. Numerical results show that the presented method is interesting.

关键词： Rank-One Update Global Convergence Nonlinear Equations Descent Direction

A Look at the Tool of BYRD and NOCEDAL

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American Journal of Computational Mathematics 2011年第4期1卷 240-246页

作者： Linghua Huang Guoyin Li gonglin yuan 不详

A power tool for the analysis of quasi-Newton methods has been proposed by Byrd and Nocedal ([1], 1989). The purpose of this paper is to make a study to the basic property (BP) given in [1]. As a result of the BP, a sufficient condition of global convergence for a class of quasi-Newton methods for solving unconstrained minimization problems without convexity assumption is given. A modified BFGS formula is designed to match the requirements of the sufficient condition. The numerical results show that the proposed method is very encouraging.

关键词： Quasi-Newton Method Unconstrained Minimization Nonconvex Problem Global Convergence