A projected hybridization of the Hestenes–Stiefel and Dai–Yuan conjugate gradient methods with application to nonnegative matrix factorization

Hybrid conjugate gradient methods are considered as an efficient family of conjugate gradient methods to solve unconstrained optimization problems. In this work, based on the memoryless BFGS update, a convex hybridization of the Hestenes–Stiefel and Dai–Yuan conjugate parameters is presented. To put in place safeguards to protect the sufficient descent property, the given search direction is projected to the orthogonal subspace to the gradient of the objective function. The convergence analysis of the proposed method is addressed under standard assumptions for general functions. The practical merits of the proposed method are computationally demonstrated on a set of CUTEr test functions as well as the well-known nonnegative matrix factorization problem.