NONMONOTONIC TRUST REGION PROJECTED REDUCED HESSIAN ALGORITHM WITH TWO-PIECE UPDATE FOR CONSTRAINED OPTIMIZATION

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. Furthermore, 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.