A Modified Augemented Lagrangian Method for a Class of Nonlinear Ill-Posed Problems

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.