Non-Monotone Trust Region Method Combined with Line Search Strategy

Yunfeng ZHANG, Qinghua ZHOU

College of Mathematics and Information Science, Hebei University, Baoding, China

Abstract: This paper revises some trust-region methods equipped with non-monotone strategies for solving unconstrained optimization problems. Unlike the traditional non-monotone trust-region method, our proposed algorithm avoids resolving the sub-problem whenever a trial step is rejected. Instead, it performs a nonmonotone Armijo-type line search in direction of the rejected trial step to construct a new point. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions.

Keywords: Unconstrained optimization; Trust-region method; Armijo-type line search; Non-monotone technique