A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization (Journal of Computational Mathematics, 2020)
A new adaptive subspace minimization three-term conjugate gradient algorithm withnonmonotone line search is introduced and analyzed in this paper. The search directionsare computed by minimizing a quadratic approximation of the objective function on specialsubspaces, and we also proposed an adaptive rule for choosing different searching directionsat each iteration. We obtain a significant conclusion that the each choice of the searchdirections satisfies the sufficient descent condition. With the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functionsunder some mild assumptions. Numerical experiments show that the proposed algorithmis promising for the given test problem set.