Numerical experience with the truncated Newton method for unconstrained optimization
Journal of Optimization Theory and Applications
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Matrix computations (3rd ed.)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Theoretical efficiency of an inexact Newton method
Journal of Optimization Theory and Applications
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
An improved inexact Newton method
Journal of Global Optimization
| Hi-index | 0.00 |
We consider solving an unconstrained optimization problem by Newton-PCG like methods in which the preconditioned conjugate gradient method is applied to solve the Newton equations. The main question to be investigated is how efficient Newton-PCG like methods can be from theoretical point of view. An algorithmic model with several parameters is established. Furthermore, a lower bound of the efficiency measure of the algorithmic model is derived as a function of the parameters. By maximizing this lower bound function, the parameters are specified and therefore an implementable algorithm is obtained. The efficiency of the implementable algorithm is compared with Newton's method by theoretical analysis and numerical experiments. The results show that this algorithm is competitive.