A Momentum Trust-Region Algorithm for Unconstrained Optimization

We introduce a Momentum Trust-Region Algorithm for unconstrained optimization that incorporates Nesterov-type acceleration into the classical trust-region framework. The method builds trust-region models around a momentum-shifted point and uses an Armijo-type backtracking procedure to safeguard progress along the resulting displacement. This design preserves the robustness of trust-region methods while exploiting momentum to improve practical efficiency. Under standard smoothness and model-decrease assumptions, we establish global convergence to first-order stationary points. Numerical experiments on 355 functions from the S2MPJ test set show that the proposed method solves more problems and reduces both iteration counts and computational time relative to classical trust-region variants.

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