Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with conve...Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.展开更多
This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to ba...This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature. A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.展开更多
By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their metho...By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China (10871130)the Ph.D.Foundation of China Education Ministry (0527003)+1 种基金Shanghai Educational Development Foundationthe Science Foundation of Shanghai Education Committee(06A110)
文摘Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
文摘This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature. A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.
基金Project supported by the National Natural Science Foundation of China (1 9971 0 65)
文摘By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.
