Nonmonotone Quasi-Newton-based conjugate gradient methods with application to signal processing

Founded upon a sparse estimation of the Hessian obtained by a recent diagonal quasi-Newton update, a conjugacy condition is given, and then, a class of conjugate gradient methods is developed, being modifications of the Hestenes-Stiefel method. According to the given sparse approximation, the curvature condition is guaranteed regardless of the line search technique. Convergence analysis is conducted without convexity assumption, based on a nonmonotone Armijo line search in which a forgetting factor is embedded to enhance probability of applying more recent available information. Practical advantages of the method are computationally depicted on a set of CUTEr test functions and also, on the well-known signal processing problems such as sparse recovery and nonnegative matrix factorization.