A Two-piece Update Algorithm with Nonmonotonic Backtracking Technique for Constrained Optimization

We propose a two-piece update of projected Hessian algorithm with trust region method for solving nonlinear equality constrained optimization problems. To deal with large problems, a two-piece update of two-side-reduced Hessian is used to replace the full Hessian matrix. By adopting the l1 penalty function as the merit function, a nonmonotonic backtracking trust region strategy is suggested which does not require the merit function to its value in every iteration. A correction step is avoided to overcome the Maratos effect. The proposed algorithm which switchs to nonmonotonic trust region strategy possesses global convergence while maintaining one step Q-superlinear local convergence rates if at least one of the update formula is updated in each iteration.