Abstract:

A filter non-monotone trust region algorithm based on a simple quadratic model is proposed for unconstrained optimization problems. A filter technique is employed into the method, which makes the trial point of the trust region sub-problem  be taken more often. If the trial step is also rejected by the filter set, a search direction is obtained  by a fixed formula and a step size is obtained  by the non-monotonic Wolfe line search,  and thus a new iterative point is achieved. The algorithm does not resolve the trust region sub-problem, so the amount of computation is reduced.The global convergence of this new method is presented under fewer conditions. Preliminary numerical experiments show that the new method is effective.

Key words: unconstrained optimization; non-monotonic trust region algorithm; filter; simple quadratic model; global convergence