ISSN:
1070-5325
Keywords:
non-linear programming
;
sparse problems
;
equality constraints
;
inexact Newton method
;
augmented Lagrangian function
;
indefinite systems
;
indefinite preconditioners
;
conjugate gradient method
;
residual smoothing
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
An inexact Newton algorithm for large sparse equality constrained non-linear programming problems is proposed. This algorithm is based on an indefinitely preconditioned smoothed conjugate gradient method applied to the linear KKT system and uses a simple augmented Lagrangian merit function for Armijo type stepsize selection. Most attention is devoted to the termination of the CG method, guaranteeing sufficient descent in every iteration and decreasing the number of required CG iterations, and especially, to the choice of a suitable preconditioner. We investigate four preconditioners, which have 2 × 2 block structure, and prove theoretically their good properties. The efficiency of the inexact Newton algorithm, together with a comparison of various preconditioners and strategies, is demonstrated by using a large collection of test problems. © 1998 John Wiley & Sons, Ltd.
Additional Material:
4 Tab.
Type of Medium:
Electronic Resource
