A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper. The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces, and we also proposed an adaptive rule for choosing different searching directions at each iteration. We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition. With the used nonmonotone line search, we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions. Numerical experiments show that the proposed algorithm is promising for the given test problem set.