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
In this paper,a three-term derivative-free projection method is proposed for solving nonlinear monotone equations.Under someappropriate conditions,the global convergence and R-linear convergence rate of the proposed m...In this paper,a three-term derivative-free projection method is proposed for solving nonlinear monotone equations.Under someappropriate conditions,the global convergence and R-linear convergence rate of the proposed method are analyzed and proved.With no need of any derivative information,the proposed method is able to solve large-scale nonlinear monotone equations.Numerical comparisons show that the proposed method is effective.展开更多
An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system...An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.展开更多
In this paper, we propose a spectral DY-type projection method for nonlinear mono- tone system of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the proj...In this paper, we propose a spectral DY-type projection method for nonlinear mono- tone system of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differen- tiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is derivative-free and so is very suitable to solve large-scale nonlinear monotone systems. The preliminary numerical results show the feasibility and effectiveness of the proposed method.展开更多
文摘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.
文摘In this paper,a three-term derivative-free projection method is proposed for solving nonlinear monotone equations.Under someappropriate conditions,the global convergence and R-linear convergence rate of the proposed method are analyzed and proved.With no need of any derivative information,the proposed method is able to solve large-scale nonlinear monotone equations.Numerical comparisons show that the proposed method is effective.
文摘An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.
文摘In this paper, we propose a spectral DY-type projection method for nonlinear mono- tone system of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differen- tiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is derivative-free and so is very suitable to solve large-scale nonlinear monotone systems. The preliminary numerical results show the feasibility and effectiveness of the proposed method.
