A trust-region algorithm combining line search filter method with Lagrange merit function for nonlinear constrained optimization

This paper presents a trust-region algorithm which employs line search filter technique with Lagrange merit function for solving nonlinear equality constrained programming. At the current iteration, the general full trust-region subproblem is decomposed into a pair of trust-region subproblems in normal and tangential subspaces. The trial step is given by solving these two trust-region subproblems. Then, different from traditional trust-region method in which the next iterate is determined by the ratio of the actual reduction to the predicted reduction, the step size is decided by interior backtracking line search together with filter method. Consequently, the expensive computation raised by resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be reduced. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. The new method retains the global convergence to the first-order critical points under some reasonable assumptions without using a merit function. Meanwhile, by using Lagrange function in the filter, the method can overcome Maratos effect without using second order correction step and hence the superlinear local convergence is achieved. The preliminary numerical results are reported to show effectiveness of the proposed algorithm.