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
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
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 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.
