Abstract:
Many engineering problems that occur in real-life are usually con strained 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 opti mization 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-Ribiére-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.
