This paper proposes a two-piece update of projected reduced Hessian algorithm with nonmonotonic trust region strategy for solving nonlinear equality constrained optimization problems. In order to deal with large probl...This paper proposes a two-piece update of projected reduced Hessian algorithm with nonmonotonic trust region strategy for solving nonlinear equality constrained optimization problems. In order to deal with large problems, a two-piece update of twoside projected reduced Hessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as the merit function, a nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. The two-piece update of projected reduced Hessian algorithm which switches to nonmonotonic trust region technique possesses global convergence while maintaining a two-step Q-superlinear local convergence rate under some reasonable conditions. Fttrthermore, one step Q-superlinear local convergence rate can be obtained if at least one of the update formulas is updated at each iteration by an alternative update rule. The numerical experiment results are reported to show the effectiveness of the proposed algorithm.展开更多
基金Supported by the National Science Foundation of China（10671126） Supported by the Shanghai Municipal Government Project（S30501）+3 种基金 Supported by the Innovation Fund Project for Graduate Student of Shanghai（JWCXSL1001） Supported by the Youth Foundation of Henan Polytechnic University（Q20093） Supported by the Applied Mathematics Provinciallevel Key Discipline of Henan Province Supported by Operational Research and Control Theory Key Discipline of Henan Polytechnic University
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 algorithm with nonmonotonic trust region strategy for solving nonlinear equality constrained optimization problems. In order to deal with large problems, a two-piece update of twoside projected reduced Hessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as the merit function, a nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. The two-piece update of projected reduced Hessian algorithm which switches to nonmonotonic trust region technique possesses global convergence while maintaining a two-step Q-superlinear local convergence rate under some reasonable conditions. Fttrthermore, one step Q-superlinear local convergence rate can be obtained if at least one of the update formulas is updated at each iteration by an alternative update rule. The numerical experiment results are reported to show the effectiveness of the proposed algorithm.
