A three-term conjugate gradient method with accelerated subspace quadratic optimization

In this paper, a general search direction of three-term conjugate gradient method which always satisfy sufficient descent condition is adopted. By solving a new accelerated subspace quadratic optimization problem which can take the advantages of the linear conjugate gradient method, a new conjugate parameter is obtained and a new truncation strategy is proposed to modify the conjugate parameter. Thus, a three-term conjugate gradient method for solving unconstrained optimization problem is proposed under the standard Wolfe line search technique. Under general assumption, the global convergence of the algorithm is discussed and obtained. Finally, the numerical performance for our method is reported via testing about 100 examples and comparing with other two algorithms. Numerical results show that the proposed method is promising.