Adaptive Regularized Quasi-Newton Method Using Inexact First-Order Information (Journal of Computational Mathematics, 2024)
Classical quasi-Newton methods are widely used to solve nonlinear problems in whichthe first-order information is exact. In some practical problems, we can only obtain approximate values of the objective function and its gradient. It is necessary to design optimization algorithms that can utilize inexact first-order information. In this paper, we proposean adaptive regularized quasi-Newton method to solve such problems. Under some mildconditions, we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method. Detailed implementations of our method, includingthe subspace technique to reduce the amount of computation, are presented. Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method isa promising method, which can utilize the inexact first-order information effectively.
Keywords: Inexact first-order information; Regularization; Quasi-Newton method.