A two-piece update of projected Hessian algorithm with nonmonotonic trust region method for constrained optimization

Abstract

In this paper we propose a two-piece update of projected Hessian algorithm with trust region method for solving nonlinear equality constrained optimization problems. In order to deal with large scale problems, a two-piece update of two side reduced Hessian is used to replace full Hessian matrix. By adopting the l 1 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 calculation of a correction step, which is necessary from theoretical point to overcome Maratos effect but sometime brings in negative results in practice, is avoided in most cases by setting a criterion to judge its necessity. The proposed algorithm which switches to nonmonotonic trust region strategy possess global convergence while maintaining one-step Q-superlinear local convergence rates if at least one of the update formula is updated at each iteration. The numerical experiment is reported to show the effectiveness of the proposed algorithms.