Updating the Multipliers Associated with Inequality Constraints in an Augmented Lagrangian Multiplier Method

Abstract

This paper contributes to the development of the field of augmented Lagrangian multiplier methods for general nonlinear programming by introducing a new update for the multipliers corresponding to inequality constraints. The update maintains naturally the nonnegativity of the multipliers without the need for a positive-orthant projection, as a result of the verification of the first-order necessary conditions for the minimization of a modified augmented Lagrangian penalty function.