Abstract
Classical nonmonotone algorithms for continuous optimization rely on a fixed memory length, meaning they always consider a specific number of recent iterations. Our approach, in contrast, explores the dynamic adjustment of this storage factor in the context of a trust region method. Specifically, in our algorithm, the nonmonotonicity memory length is directly adapted based on the local noisy behavior of the cost function, quantified using the arithmetic–geometric mean inequality. We also propose adaptive strategies for setting the trust region radius by leveraging several recent scalar estimations of the second-order information of the model. These estimations are based on ellipsoid norm least-squares approximations of the secant equation, rather than the traditional Euclidean norm-based schemes. Incorporating such algorithmic improvements, we introduce a dynamically nonmonotone trust region algorithm and analyze its theoretical properties, specifically the global convergence. To validate our theoretical developments, we conduct numerical experiments evaluating the performance of the proposed algorithm on both benchmark test problems from the literature and real-world binary classification tasks in the presence of outliers. The computational results confirm the practical efficiency of the proposed trust region algorithm.