TITLE:
A Modified Augemented Lagrangian Method for a Class of Nonlinear Ill-Posed Problems
AUTHORS:
Mhbm Shariff
KEYWORDS:
Iterative Method; Nonlinear; Ill-conditioned; Large Parameter Values; Large-scale
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.3 No.1B1,
July
11,
2013
ABSTRACT: A class of nonlinear problems with real parameters is
defined. Generally, in this class of problems, when the parametric values are
very large, the problems become ill-posed and numerical difficulties are
encountered when trying to solve these problems. In this paper, the nonlinear
problems are reformulated to overcome the numerical difficulties associated
with large parametric values. A novel iterative algorithm, which is suitable
for large scale problems and can be easily parallelized, is proposed to solve
the reformulated problems. Numerical tests indicate that the proposed algorithm
gives stable solutions. Convergence properties of the proposed algorithm are
investigated. In the limiting case, when the corresponding constraint is
exactly satisfied, the proposed method is equivalent to the standard augmented
Lagrangian method.