A Lagrange function for solving nonlinear optimization problem with constraints

Abstract

This paper proposes a nonlinear Lagrangian for solving optimization problems with inequality constraints, and discusses properties of the function at the Karush-Kuhn-Tucker (KKT) points. The local convergence of the sequence of iterate points generated based on the proposed nonlinear Lagrangian is shown, when the penal parameter is larger than a threshold under a set of suitable conditions on problem functions, and the error estimate for the solution is given, which depends on the penalty parameter. Key words: Nonlinear Lagrangian function, nonlinear optimization, convergence.