  In this paper, based on the limited memory techniques and subspace
minimization conjugate gradient (SMCG) methods, a regularized limited memory
subspace minimization conjugate gradient method is proposed, which contains two
types of iterations. In SMCG iteration, we obtain the search direction by
minimizing the approximate quadratic model or approximate regularization model.
In RQN iteration, combined with regularization technique and BFGS method, a
modified regularized quasi-Newton method is used in the subspace to improve the
orthogonality. Moreover, some simple acceleration criteria and an improved
tactic for selecting the initial stepsize to enhance the efficiency of the
algorithm are designed. Additionally, an generalized nonmonotone line search is
utilized and the global convergence of our proposed algorithm is established
under mild conditions. Finally, numerical results show that, the proposed
algorithm has a significant improvement over ASMCG_PR and is superior to the
particularly well-known limited memory conjugate gradient software packages
CG_DESCENT (6.8) and CGOPT(2.0) for the CUTEr library.
