This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problem...This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.展开更多
This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programmin...This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.展开更多
基金The author gratefully acknowledges the partial supports of the National Science Foundation of China Grant (10071050)Science Foundation of Shanghai Technical Sciences Committee Grant (02ZA14070) Science Foundation of Shanghai Education Committee Grant
文摘This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.
基金the National Natural Science Foundation of China ( 1 0 4 71 0 94) ,the ScienceFoundation of Shanghai Technical Sciences Committee ( 0 2 ZA1 40 70 ) and the Science Foundation ofShanghai Education Committee( 0 2 DK0 6)
文摘This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.
