Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient m...Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.展开更多
This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-o...This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.展开更多
In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties： 1） The search direc...In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties： 1） The search direction is always a sufficiently descent direction at every iteration without the line search used; 2） The search direction always satisfies the angle property, which is independent of the convexity of the objective function. Under mild conditions, the authors prove that the proposed method has global convergence, and its convergence rate is also investigated. The numerical results show that the new descent memory method is efficient for the given test problems.展开更多
In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-un...In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.展开更多
In this paper,a new modified BFGS method without line searches is proposed.Unlike traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and Zhan...In this paper,a new modified BFGS method without line searches is proposed.Unlike traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and Zhang.Under some suitable assumptions,the global convergence andthe superlinear convergence of the new algorithm are established,respectively.And some preliminarynumerical experiments,which shows that the new Algorithm is feasible,is also reported.展开更多
文摘Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.
基金Supported by the Scientific Research Foundation of Hunan Provincial Education Department(02B021) Hunan Provincial Natural Science Foundation,China(03JJY6002)
文摘This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.
基金supported by the National Science Foundation of China under Grant No.70971076the Foundation of Shandong Provincial Education Department under Grant No.J10LA59
文摘In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties： 1） The search direction is always a sufficiently descent direction at every iteration without the line search used; 2） The search direction always satisfies the angle property, which is independent of the convexity of the objective function. Under mild conditions, the authors prove that the proposed method has global convergence, and its convergence rate is also investigated. The numerical results show that the new descent memory method is efficient for the given test problems.
文摘In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.
基金supported by the Foundation of National Natural Science Foundation of China under Grant No. 10871226the Natural Science Foundation of Shandong Province under Grant No. ZR2009AL006+1 种基金the Development Project Foundation for Science Research of Shandong Education Department under Grant No. J09LA05the Science Project Foundation of Liaocheng University under Grant No. X0810027
文摘In this paper,a new modified BFGS method without line searches is proposed.Unlike traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and Zhang.Under some suitable assumptions,the global convergence andthe superlinear convergence of the new algorithm are established,respectively.And some preliminarynumerical experiments,which shows that the new Algorithm is feasible,is also reported.
