A Subspace Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization.

In this paper, a subspace three-term conjugate gradient method is proposed. The search directions in the method are generated by minimizing a quadratic approximation of the objective function on a subspace. And they satisfy the descent condition and Dai-Liao conjugacy condition. At each iteration, the subspace is spanned by the current negative gradient and the latest two search directions. Thereby, the dimension of the subspace should be 2 or 3. Under some appropriate assumptions, the global convergence result of the proposed method is established. Numerical experiments show the proposed method is competitive for a set of 80 unconstrained optimization test problems.