A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization With Applications.

Ensuring the positive definiteness and avoiding ill conditioning of the Hessian update in the stochastic Broyden-Fletcher-Goldfarb-Shanno (BFGS) method are significant in solving nonconvex problems. This article proposes a novel stochastic version of a damped and regularized BFGS method for addressing the above problems. While the proposed regularized strategy helps to prevent the BFGS matrix from being close to singularity, the new damped parameter further ensures the positivity of the product of correction pairs.