J. Math. Comput. Sci.

The quasi-Newton (QN) method are among the efficient variants of conjugate gradient (CG) method for solving unconstrained optimization problems. The QN method utilizes the gradients of the function while ignoring the available value information at every iteration. In this paper, we extended the Dai-Yuan [39] coefficient in designing a new CG method for large-scale unconstrained optimization problems. An interesting feature of our method is that its algorithm not only uses the available gradient value, but also consider the function value information. The global convergence of the proposed method was established under some suitable Wolfe conditions. Extensive numerical computation have been carried out which show that the average performance of this new algorithm is efficient and promising. In addition, the proposed method was extended to solve practical application problem of portfolio selection.

A variant of Dai-Yuan conjugate gradient method for unconstrained optimization and its application in portfolio selection