A scalar Hessian estimation with a sparse nonmonotone line search technique for the sparse recovery problem

Abstract

Employing the scaled memoryless BFGS (Broyden-Fletcher-Goldfarb-Shanno) updating formula, a multiplier of the identity matrix is proposed as an estimation of the inverse Hessian of the objective function. Incorporated into the proximal operator, the suggested spectral gradient vector has been employed to solve the nonsmooth sparse recovery problem. Taking sparsity property into consideration, a nonmonotone backtracking line search technique is put forward which is adjusted for the nonsmooth sparse recovery cost function. Convergence of the algorithm is analyzed based on the given line search. Ultimately, computational advantages of the algorithm are depicted on a class of randomly generated test problems as well as a set of the CUTEr functions.