Abstract:

Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which espectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate  gradient methods, the new methods take both available gradient and function value information. Furthermore,
their modifications are proposed. These methods are shown to be global convergent under some assumptions. Numerical results are also reported.

Key words: conjugate gradient, unconstrained optimization, global convergence, conjugacy condition