A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on...A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on variables is proposed. In order to deal with large problems, a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem. The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint. Both trust region strategy and line search technique at each iteration switch to obtaining a backtracking step generated by the two trust region subproblems. By adopting the l 1 penalty function as the merit function, the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion and the second order correction step are used to overcome Maratos effect and speed up the convergence progress in some ill-conditioned cases. MR Subject Classification 90C30 - 65K05 - 49M40 Keywords trust region method - backtracking step - reduced Hessian - nonmonotonic technique - interior point Supported partially by the National Natural Science Foundation of China (10071050), Science Foundation (02ZA14070) of Shanghai Technical Sciences Committee and Science Foundation (02DK06) of Shanghai Education Committee.展开更多
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introd...In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.展开更多
基金Supported partially by the National Natural Science Foundation of China( 1 0 0 71 0 5 0 ) ScienceFoundation ( 0 2 ZA1 4 0 70 ) of Shanghai Technical Sciences Committee and Science Foundation ( 0 2 DK0 6) ofShanghai Education Committee.
文摘A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on variables is proposed. In order to deal with large problems, a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem. The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint. Both trust region strategy and line search technique at each iteration switch to obtaining a backtracking step generated by the two trust region subproblems. By adopting the l 1 penalty function as the merit function, the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion and the second order correction step are used to overcome Maratos effect and speed up the convergence progress in some ill-conditioned cases. MR Subject Classification 90C30 - 65K05 - 49M40 Keywords trust region method - backtracking step - reduced Hessian - nonmonotonic technique - interior point Supported partially by the National Natural Science Foundation of China (10071050), Science Foundation (02ZA14070) of Shanghai Technical Sciences Committee and Science Foundation (02DK06) of Shanghai Education Committee.
基金supported by National Natural Science Foundation of China (Grant No. 10871098)Science Foundation of Jiangsu Province (Grant No. BK2006214)
文摘In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
