A PRP-HS Type Hybrid Nonlinear Conjugate Gradient Method for Solving Unconstrained Optimization Problems

Many engineering problems that occur in real-life are usually constrained by one or more factors which constitute the basis for the complexity of obtaining optimal solutions. While some of these problems may be transformed to the unconstrained forms, there is a large pool of purely unconstrained optimization problems in engineering which have practical applications in the industry. One effective approach for solving this latter category of problems is the nonlinear conjugate gradient method (NCGM). Particularly, the NCGM uses an efficient recursive scheme to solve unconstrained optimization problems with very large dimensions. In this paper, a new hybrid NCGM is proposed based on the recent modifications of the Polak-Ribiere-Polyak (PRP) and Hestenes-Stiefel (HS) methods. Theoretical analyses and numerical computations using standard benchmark functions, as well as comparison with existing NCGM schemes show that the proposed PRP-HS type hybrid scheme is globally convergent and computationally efficient.