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An Adaptive Spectral Conjugate Gradient Method with Restart Strategy
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作者 Zhou Jincheng Jiang Meixuan +2 位作者 Zhong Zining Wu Yanqiang Shao Hu 《数学理论与应用》 2024年第3期106-118,共13页
As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall... As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective. 展开更多
关键词 Unconstrained optimization Spectral conjugate gradient method Restart strategy Inexact line search Global convergence
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NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD 被引量:2
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作者 LING Guo-ping(凌国平) +1 位作者 FANG Jian-wen(方健雯) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1089-1096,共8页
A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently so... A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme ( MILU-CG). The effects of surface suction or blowing' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too. 展开更多
关键词 circular cylinder with surface suction or blowing separated vortex flow around bluff body and its control vorticity-velocity method preconditioned conjugate gradient method
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A modified three–term conjugate gradient method with sufficient descent property 被引量:1
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作者 Saman Babaie–Kafaki 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第3期263-272,共10页
A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysi... A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method. 展开更多
关键词 unconstrained optimization conjugate gradient method EIGENVALUE sufficient descent condition global convergence
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High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations 被引量:1
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作者 李根 唐春安 李连崇 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第10期1225-1236,共12页
Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering (CAE) and computer aided manufacturing ... Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering (CAE) and computer aided manufacturing (CAM). This paper presents a high-efficiency improved symmetric successive over-relaxation (ISSOR) preconditioned conjugate gradient (PCG) method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance. 展开更多
关键词 improved preconditioned conjugate gradient (PCG) method conjugate gradient method large-scale linear equation finite element method
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Subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization 被引量:1
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作者 Ting Zhao Hongwei Liu 《Journal of Harbin Institute of Technology(New Series)》 CAS 2021年第5期61-69,共9页
Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology ... Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods. 展开更多
关键词 cubic regularization model conjugate gradient method subspace technique unconstrained optimization
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Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations 被引量:1
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作者 SUN Qing-ying(Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China Department of Applied Mathematics, University of Petroleum , Dongying 257061, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期154-162,共9页
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS met... Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method. 展开更多
关键词 nonlinear programming restarting conjugate gradient method forcing function reverse modulus of continuity function CONVERGENCE
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A New Nonlinear Conjugate Gradient Method for Unconstrained Optimization Problems 被引量:1
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作者 LIU Jin-kui WANG Kai-rong +1 位作者 SONG Xiao-qian DU Xiang-lin 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第3期444-450,共7页
In this paper,an efficient conjugate gradient method is given to solve the general unconstrained optimization problems,which can guarantee the sufficient descent property and the global convergence with the strong Wol... In this paper,an efficient conjugate gradient method is given to solve the general unconstrained optimization problems,which can guarantee the sufficient descent property and the global convergence with the strong Wolfe line search conditions.Numerical results show that the new method is efficient and stationary by comparing with PRP+ method,so it can be widely used in scientific computation. 展开更多
关键词 unconstrained optimization conjugate gradient method strong Wolfe line search sufficient descent property global convergence
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Global Convergence of a New Restarting Three Terms Conjugate Gradient Method for Non-linear Optimizations 被引量:1
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作者 SUN Qing-ying SANG Zhao-yang TIAN Feng-ting 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期69-76,共8页
In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global conv... In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved. 展开更多
关键词 nonlinear programming restarting three terms conjugate gradient method forcing function reverse modulus of continuity function convergence
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Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations 被引量:1
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作者 Michael K.Ng 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第4期461-474,共14页
Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image... Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well. 展开更多
关键词 Edge-preserving image restoration multiplicative half-quadratic regularization Newton method preconditioned conjugate gradient method constraint preconditioner eigenvalue bounds
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An Efficient Projected Gradient Method for Convex Constrained Monotone Equations with Applications in Compressive Sensing 被引量:1
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作者 Yaping Hu Yujie Wang 《Journal of Applied Mathematics and Physics》 2020年第6期983-998,共16页
In this paper, a modified Polak-Ribière-Polyak conjugate gradient projection method is proposed for solving large scale nonlinear convex constrained monotone equations based on the projection method of Solodov an... In this paper, a modified Polak-Ribière-Polyak conjugate gradient projection method is proposed for solving large scale nonlinear convex constrained monotone equations based on the projection method of Solodov and Svaiter. The obtained method has low-complexity property and converges globally. Furthermore, this method has also been extended to solve the sparse signal reconstruction in compressive sensing. Numerical experiments illustrate the efficiency of the given method and show that such non-monotone method is suitable for some large scale problems. 展开更多
关键词 Projection method Monotone Equations Conjugate Gradient method Compressive Sensing
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Calculation method of sliding ratios for conjugate-curve gear pair and its application 被引量:3
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作者 梁栋 陈兵奎 高艳娥 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第3期946-955,共10页
The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The gen... The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The general calculation formulas of sliding ratios are developed according to the conjugate curves. The applications to the circular arc gears based on conjugate curves and the novel involute-helix gears are studied. A comparison on the sliding coefficient with the conventional corresponding gear drive is also carried out. The influences of gear parameters such as spiral parameter, gear ratio and modulus on the sliding ratios of gear drive are discussed. Brief description of manufacturing method for conjugate-curve gear pair is given. The research results show that the sliding ratios of gear pair become smaller with the increase of spiral parameter and gear ratio, respectively. And it will be greater with the increase of modulus for the tooth profiles. The meshing characteristics of conjugate-curve gears are further reflected and the optimization design of tooth profiles with high performance may be obtained. 展开更多
关键词 conjugate-curve gear conjugate curve sliding ratio manufacturing method
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A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems 被引量:2
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作者 Zhimin Liu Shouqiang Du Ruiying Wang 《Journal of Applied Mathematics and Physics》 2016年第6期1024-1031,共8页
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje... In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported. 展开更多
关键词 Stochastic Generalized Linear Complementarity Problems Fischer-Burmeister Function Conjugate Gradient Projection method Global Convergence
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Streamline upwind finite element method for conjugate heat transfer problems 被引量:3
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作者 Niphon Wansophark Atipong Malatip Pramote Dechaumphai 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第5期436-443,共8页
This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite el... This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method. 展开更多
关键词 Streamline upwind.Conjugate heat transfer.Finite element method
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GLOBAL CONVERGENCE OF THE GENERAL THREE TERM CONJUGATE GRADIENT METHODS WITH THE RELAXED STRONG WOLFE LINE SEARCH
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作者 Xu Zeshui Yue ZhenjunInstitute of Sciences,PLA University of Science and Technology,Nanjing,210016. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第1期58-62,共5页
The global convergence of the general three term conjugate gradient methods with the relaxed strong Wolfe line search is proved.
关键词 Conjugate gradient method inexact line search global convergence.
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IMPROVED PRECONDITIONED CONJUGATE GRADIENT METHOD AND ITS APPLICATION IN F.E.A.FOR ENGINEERING
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作者 郑宏 葛修润 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第4期371-380,共10页
In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the ite... In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations. 展开更多
关键词 preconditioned conjugate gradient method finite element ill-conditioned problems
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MILU-CG METHOD AND THE NUMERICAL STUDY ON THE FLOW AROUND A ROTATINGCIRCULAR CYLINDER
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作者 凌国平 凌国灿 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第8期783-792,共10页
A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient meth... A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states. 展开更多
关键词 rotating circular cylinder vortex pattern finite difference method preconditioned conjugate gradient method incomplete LU decomposition
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An Inexact Halley's Method
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作者 闫桂峰 田祥 《Journal of Beijing Institute of Technology》 EI CAS 2005年第3期340-343,共4页
An inexact Halley's method-Halley-PCG(preconditioned conjugate gradient) method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by prec... An inexact Halley's method-Halley-PCG(preconditioned conjugate gradient) method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by preconditioned conjugate gradient method approximately. The convergence result is given and the efficiency of the method compared to the improved Halley's method is shown. 展开更多
关键词 unconstrained optimization problems improved Halley's method preconditioned conjugate gradient method
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A Descent Gradient Method and Its Global Convergence
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作者 LIU Jin-kui 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期142-150,共9页
Y Liu and C Storey(1992)proposed the famous LS conjugate gradient method which has good numerical results.However,the LS method has very weak convergence under the Wolfe-type line search.In this paper,we give a new de... Y Liu and C Storey(1992)proposed the famous LS conjugate gradient method which has good numerical results.However,the LS method has very weak convergence under the Wolfe-type line search.In this paper,we give a new descent gradient method based on the LS method.It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search.Finally,we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP^+method. 展开更多
关键词 unconstrained optimization conjugate gradient method strong Wolfe line search sufficient descent property global convergence
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PRECONDITIONED METHODS FOR SPACE-TIME ADAPTIVE PROCESSING
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作者 Zhang Zenghui Hu Weidong Yu Wenxian 《Journal of Electronics(China)》 2008年第4期465-470,共6页
This paper introduces the preconditioned methods for Space-Time Adaptive Processing(STAP).Using the Block-Toeplitz-Toeplitz-Block(BTTB)structure of the clutter-plus-noise covari-ance matrix,a Block-Circulant-Circulant... This paper introduces the preconditioned methods for Space-Time Adaptive Processing(STAP).Using the Block-Toeplitz-Toeplitz-Block(BTTB)structure of the clutter-plus-noise covari-ance matrix,a Block-Circulant-Circulant-Block(BCCB)preconditioner is constructed.Based on thepreconditioner,a Preconditioned Multistage Wiener Filter(PMWF)which can be implemented by thePreconditioned Conjugate Gradient(PCG)method is proposed.Simulation results show that thePMWF has faster convergence rate and lower processing rank compared with the MWF. 展开更多
关键词 Conjugate gradient method Multistage Wiener filter PRECONDITIONER Space-Time Adaptive Processing (STAP)
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The Conjugate Gradient Method in Random Variables
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作者 HSU Ming-hsiu LAI King-fai 《Chinese Quarterly Journal of Mathematics》 2021年第2期111-121,共11页
We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
关键词 Riesz algebra MATRICES Measurable functions Ordered structures Conjugate gradient methods Computational methods in function algebras
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