Abstract:

With the existing conjugate gradient method, the search directions of two hybrid conjugate gradient methods were modified, such that the new hybrid conjugate gradient methods can automatically generate sufficient descent direction independent of the line search used for each iteration. Under appropriate conditions and the Wolfe line search, it was proved that the new methods are globally convergent. Preliminary numerical results show that the methods are efficient.

Key words:  unconstrained optimization; conjugate gradient methods; sufficient descent property; global convergence