Nonmonotone trust region method for solving optimization problems

Abstract

In this paper a trust region (TR) method with nonmonotone technique for optimization is proposed. We construct a new ratio of actual descent and predicted descent which is a simple and natural generalization of the modified Armijo line search rule. The paper exposes the relationship between the trust region method and line search approach. Since this method possesses the robust properties of trust region subproblem, it is globally convergent although we employ the nonmonotone sequence of function values instead of the monotone sequence. In addition, the proof of convergence is obviously simpler than one of Newton-type method with nonmonotone line search. Finally, applications of the nonmonotone TR algorithm to some optimization problems are discussed.