A new subspace minimization conjugate gradient method based on tensor model for unconstrained optimization

A new subspace minimization conjugate gradient method based on tensor model is proposed and analysed. If the objective function is close to a quadratic, we construct a quadratic approximation model in a two-dimensional subspace to generate the search direction; otherwise, we construct a tensor model. It is remarkable that the search direction satisfies the sufficient descent property. We prove the global convergence of the proposed method under mild assumptions. Numerical comparisons are given with well-known CGOPT and CG_DESCENT and show that the proposed algorithm is very promising.