Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems

作     者：Ladislav Lukšan Jan Vlček 

作者机构：Institute of Computer Science Academy of Sciences of the Czech Republic Pod vodárenskou věží 2 182 07 Prague 8 Czech Republic 

出 版 物：《Numerical Linear Algebra with Applications》 

年 卷 期：1999年第5卷第3期

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：non-linear programming sparse problems equality constraints inexact Newton method augmented Lagrangian function indefinite systems indefinite preconditioners conjugate gradient method residual smoothing 

摘      要：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.