We consider the unary optimization problem: minf(x)=Σi=1 mUi(αi(x)),x∈Rn, where Ui(·) is a function of a single argument and αi(x) = aT ix, ai∈Rn, i=1,2,...,m. We investigate the inexact Newton methods with three techniques: Cholesky factorization, rank-1 update and preconditioned conjugate gradient subiteration. Based on the special structure of unary optimization problems, the relationship between efficiency of the inexact Newton method and combination of the above techniques is analyzed. We also develop implementable algorithms by attempting to find a near-optimal combination. The corresponding numerical results are reported.
