TY - JOUR
T1 - A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization
AU - Zhang , Keke
AU - Liu , Hongwei
AU - Liu , Zexian
JO - Journal of Computational Mathematics
VL - 2
SP - 159
EP - 177
PY - 2020
DA - 2020/11
SN - 39
DO - http://doi.org/10.4208/jcm.1907-m2018-0173
UR - https://global-sci.org/intro/article_detail/jcm/18369.html
KW - Conjugate gradient method, Nonmonotone line search, Subspace minimization, Sufficient descent condition, Global convergence.
AB - <p style="text-align: justify;">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.</p>