AS-BOX: Additional Sampling Method for  Weighted Sum Problems with Box Constraints

A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (\text{A}ddi\-ti\-onal \text{S}ampling for \text{BOX} constraints), that combines projected gradient directions with adaptive variable sample size strategies and nonmonotone line search. The method dynamically adjusts the batch size based on progress with respect to the additional sampling function and on structural consistency of the projected direction, enabling practical adaptivity of AS-BOX, while ensuring theoretical support. We establish almost sure convergence under standard assumptions and provide complexity bounds. Numerical experiments demonstrate the efficiency and competitiveness of the proposed method compared to state-of-the-art algorithms. MSC Classification: 90C15,90C26, 90C30, 65K05