Global convergence of a nonmonotone filter method for equality constrained optimization

In this paper, we present a global convergence theory for a class of nonmonotone filter trust region methods. At each iteration, the trial step is decomposed into a quasi-normal step and a tangential step. Comparable to the traditional filter and monotone methods, the new approach is more flexible and less computational scale. Under some reasonable conditions, we show that there exists at least one accumulate point of the sequence of iterates that is a KKT point. (C) 2012 Elsevier Inc. All rights reserved.