A nonmonotone filter trust region method for nonlinear constrained optimization

Abstract

In this paper, we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. Similar to Bryd-Omojokun class of algorithms, each step is composed of a quasi-normal step and a tangential step. This new method has more flexibility for the acceptance of the trial step compared to the filter methods, and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the globally convergence properties. Numerical tests are presented that confirm the efficiency of the approach.

Global Convergence of a New Nonmonotone Filter Method for Equality Constrained Optimization

“…From (A1), (A2), and (A3), it exists a constant ] such that Proof. It is similar to the proof of Lemma 2 in [13].…”

“…M. Ulbrich and S. Ulbrich [12] proposed a class of penalty-function-free nonmonotone trust region methods for nonlinear equality constrained optimization without filter technique. Su and Pu [13] introduced a nonmonotone trust region method which used the nonmonotone technique in the traditional filter criteria. Su and Yu [14] presented a nonmonotone method without penalty function or filter.…”

“…Similar to the Byrd-Omojokun class of algorithms, each step is decomposed into the sum of two distinct components, a quasi-normal step and a tangential step. The main contribution of our paper is to employ the nonmonotone idea to the dominated area of the filter so that the new and more flexible criteria is given, which is different from that of Gould and Toint [15] and Su and Pu [13].…”

A kind of nonmonotone filter method for nonlinear complementarity problem

“…It has no demand on the initial point. By means of nonmonotone filter which proposed by Ke Su and Dingguo Pu [25], the restoration phase, a common feature of the large majority of the filter methods, is not needed. And compared with traditional filter methods, the acceptance of trial step is more flexible by use of nonmonotone filter technique.…”

Global and local convergence of a nonmonotone trust region algorithm for equality constrained optimization

“…Over the last decades, the nonmonotone technique has been combined with trust region method to deal with unconstrained and constrained optimization problems [13,14,6,[15][16][17][18][19]. More recently, the nonmonotone trust region method without penalty function has also been developed for constrained optimization [20][21][22].…”