A stochastic extra-step quasi-Newton method for nonsmooth nonconvex optimization

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve class of nonsmooth nonconvex composite optimization problems. We assume that the gradient smooth part objective function can only be approximated by oracles. The proposed combines general higher order steps derived from an underlying proximal type fixed-point equation with additional guarantee convergence. Based on suitable bounds step sizes, we establish global convergence stationary points in expectation and extension approach using variance reduction techniques discussed. Motivated large-scale big data applications, investigate coordinate-type scheme allows generate cheap tractable directions. Finally, numerical results logistic regression deep learning problems show our algorithm compares favorably other state-of-the-art methods.