Abstract:

The conjugate gradient method is one of the most effective methods for solving large-scale unconstrained optimization. Combining the second inequality of the strong Wolfe line search, two new conjugate parameters are constructed. Under usual assumptions, it is proved that the improved PRP and HS conjugate gradient methods satisfy sufficient descent condition with the greater range of parameter in the strong Wolfe line search and converge globally for unconstrained optimization. Finally, two group numerical experiments for the proposed methods and their comparisons are tested, the numerical results and their corresponding performance files are reported, which show that the proposed methods are promising.

Key words: Unconstrained optimization, Conjugate gradient method, Strong Wolfe line search, Global convergence