An ODE-type Filter-Trust-Region Algorithm for Solving Nonlinear Programming

Based on the filter technique, this paper presents an ODE-type filter-trust-region algorithm for solving nonlinear inequality constrained optimization problems. One feature of the proposed method is that only a system of linear equations is solved to obtain a search direction at each iteration, thus avoiding solving a quadratic programming sub-problem with a trust region bound. Another feature is that this method dispenses with the idea of penalty function and thus avoiding the difficult choice of penalty parameters. Under some standard assumptions, the iterate sequence generated by the algorithm converges superlinearly. Numerical results are also reported.