New version of the three-term conjugate gradient method based on spectral scaling conjugacy condition that generates descent search direction

In this paper, a general form of three-term conjugate gradient method is presented, in which the search directions simultaneously satisfy the Dai-Liao conjugacy condition and sufficient descent property. In addition, the choice for an optimal parameter is suggested in the sense that the condition number of the iteration matrix could arrives at its minimum, which can be regarded as the inheritance and development of the spectral scaling quasi-Newton equation. Different from the existent methods, a new update strategy in constructing the search direction is proposed to establish the global convergence for the general function. Numerical results show our algorithm is practical and effective for the test problems.