A second-order convergence augmented Lagrangian method using non-quadratic penalty functions

Abstract

The purpose of the present paper is to study the global convergence of a practical Augmented Lagrangian model algorithm that considers non-quadratic Penalty–Lagrangian functions. We analyze the convergence of the model algorithm to points that satisfy the Karush–Kuhn–Tucker conditions and also the weak second-order necessary optimality condition. The generation scheme of the Penalty–Lagrangian functions includes the exponential penalty function and the logarithmic-barrier without using convex information.