A subspace conjugate gradient algorithm for large-scale unconstrained optimization (Q1681785)

A subspace three-term conjugate gradient method using subspace technique is presented. The search directions in the method are generated by minimizing a quadratic approximation of the objective function on a subspace. At each iteration, the subspace is spanned by the current negative gradient and the latest two search directions. It is shown that the search directions satisfy the descent condition and the Dai-Liao conjugacy condition. The global convergence of the presented method with Wolfe line search is proved. Computational results for a set of 80 unconstrained optimization test problems show that the presented method is effective.