In this paper, we introduce a novel generalized subsampling Newton method designed to effectively address finite-sum optimization problems. This method is particularly effective for iterative techniques aimed at solving a system of linear inequalities in the form of \(Ax \le b\) , especially when the objective function is not necessarily twice differentiable. The implementation of this method significantly impacts increasing speed, saving resources, and optimizing system memory usage, thereby improving algorithm performance, especially on large-scale problems. The convergence of the mentioned method is proven under the conditions of convexity and Lipschitz continuity of the objective function’s gradient. Preliminary numerical experiments on large-scale generated random problems and various datasets from the UCI benchmark datasets and Netlib repositories provide empirical evidence supporting our theoretical findings of the proposed method compared to similar methods.
