Convergence to Second-Order Stationary Points of a Primal-Dual Algorithm Model for Nonlinear Programming

We define a primal-dual algorithm model (SOLA) for inequality constrained optimization problems that generates a sequence converging to points satisfying the second order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the unconstrained minimization of an exact augmented Lagrangian function and the use of a curvilinear linesearch technique which exploits information on the non convexity of the augmented Lagrangian function. AMS subject classification. 90C30.