PCG-inexact Newton methods for unary optimization
We consider the unary optimization problem: , where Ui() is a function of a single argument and . We investigate the inexact Newton methods with three techniques: Cholesky factorization, rank-1 update and preconditioned conjugate gradient (PCG) 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.
inexact newton method unary optimization cholesky factorization preconditioned conjugate gradient method efficiency coefficient