A THREE-TERM CONJUGATE GRADIENT ALGORITHM USING SUBSPACE FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION

It is well known that conjugate gradient methods are suitable for large-scale nonlinear optimization problems, due to their simple calculation and low storage. In this paper, we present a three-term conjugate gradient method using subspace technique for large-scale unconstrained optimization, in which the search direction is determined by minimizing the quadratic approximation of the objective function in a subspace which is discussed in two cases. We show the search direction can both satisfy the descent condition and Dai-Liao conjugacy condition. Under proper assumptions, global convergence result of the proposed method is established. Numerical experiments show the proposed method is efficient and robust.