A mixed conjugate gradient met with sufficient descent property for the exact line search

Conjugate gradient is an important method that is used to solve the problem of large-scale unconstrained nonlinear optimization.The structure of the parameter βk is different,which forms a kind of conjugate gradient algorithm.Based on the inspiration of existing research results,a new constructor of the parameter βk is given,then a new conjugate gradient algorithm is proposed.It is proved that the new method is of full descent under the exact line search.Meanwhile,a method of global convergence is proved under the condition that the objective function is continuously differentiable.