A new hybrid PRP-SMAR (PS) Conjugate Gradient method with sufficient descent properties for unconstrained optimization

Abstract

Conjugate gradient (CG) method has played an important role in solving unconstrained optimization. Their wide application in many fields is due to their low memory requirement and global convergence properties. Numerous studies have been done recently to improve the CG method. In this paper, an improved hybrid formula for conjugate gradient coefficient β_k (i.e.) β_k^PS = max {β_k^PRP, β_k^SMAR}) has been proposed which possesses sufficient descent the properties under exact line search. The result of the numerical experiment has shown that this new formula performs better than the classical CG methods. PRP and the recent method SMAR.