A Stochastic Inertial Limited Memory BFGS Algorithm Based on the Mathematical Model of Rural Pipeline Network and its Application in Machine Learning

Abstract

Abstract Stochastic algorithms are critical in addressing complex rural pipe networks and non-convex stochastic optimization problems. With the development of artificial intelligence, large-scale optimization problems that cannot be solved effectively by traditional optimization methods have emerged. Therefore, stochastic optimization algorithms are rapidly developing in the field of optimization. This paper introduces an inertial extrapolation stochastic BFGS (IESBFGS) algorithm, an innovative amalgamation of the inertial extrapolation technique and the finite memory quasi-Newton algorithm to solve nonconvex stochastic optimization problems. Firstly, the inertial extrapolation technique is employed to track the iteration point to the optimal x-value. Second, it is combined with a finite-memory proposed Newton algorithm thereby increasing the convergence speed. Then, the superiority of IESBFGS is verified by comparing the experimental performance with other better algorithms on machine learning SVM model and ERM model. Finally, it is shown that the algorithm offers good prospects for solving nonconvex problems.