Local analysis of a new multipliers method

In this paper we introduce a penalty function and a corresponding multipliers method for the solution of a class of nonlinear programming problems where the equality constraints have a particular structure. The class models optimal control and engineering design problems with bounds on the state and control variables and has wide applicability. The multipliers method updates multipliers corresponding to inequality constraints (maintaining their nonnegativity) instead of dealing with multipliers associated with equality constraints. The basic local convergence properties of the method are proved and a dual framework is introduced. We also analyze the properties of the penalized problem related with the penalty function.