Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function

Abstract

In the present research, an Augmented Lagrangian method with the use of the exponential penalty function for solving inequality constraints problems is considered. Global convergence is proved using the constant positive generator constraint qualification when the subproblem is solved in an approximate form. Since this constraint qualification was defined recently, the present convergence result is new for the Augmented Lagrangian method based on the exponential penalty function. Boundedness of the penalty parameters is proved considering classical conditions. Three illustrative examples are presented.