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.