An approximate Newton-type proximal method using symmetric rank-one updating formula for minimizing the nonsmooth composite functions

Abstract

Founded upon the scaled memoryless symmetric rank-one updating formula, we propose an approximation of the Newton-type proximal strategy for minimizing the nonsmooth composite functions. More exactly, to approximate the inverse Hessian of the smooth part of the objective function, a symmetric rank-one matrix is employed to straightly compute the search directions for a special category of well-known functions. Convergence of the given algorithm is argued with a nonmonotone backtracking line search adjusted for the corresponding nonsmooth model. Also, its practical advantages are computationally depicted in the two well-known real-world models.