In this paper, we proposed a spectral gradient-Newton two phase method for constrained semismooth equations. In the first stage, we use the spectral projected gradient to obtain the global convergence of the algorithm...In this paper, we proposed a spectral gradient-Newton two phase method for constrained semismooth equations. In the first stage, we use the spectral projected gradient to obtain the global convergence of the algorithm, and then use the final point in the first stage as a new initial point to turn to a projected semismooth asymptotically newton method for fast convergence.展开更多
In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale...In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.展开更多
In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of comput...In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.展开更多
A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active se...A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.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
Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by exp...Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.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
文摘In this paper, we proposed a spectral gradient-Newton two phase method for constrained semismooth equations. In the first stage, we use the spectral projected gradient to obtain the global convergence of the algorithm, and then use the final point in the first stage as a new initial point to turn to a projected semismooth asymptotically newton method for fast convergence.
基金The subject is supported by Natural Science Foundation of China and Natural Science Foundation of Shandong Province.
文摘In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.
基金Supported by the National Natural Science Foundation of China (10871130)the Research Fund for the Doctoral Program of Higher Education of China (20093127110005)the Scientific Computing Key Laboratory of Shanghai Universities
文摘In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.
基金This research was supported by Chinese NNSF grant and NSF grant of Jiangsu Province
文摘A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.10171104,10571171&40233029).
文摘Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
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.
