Convergence to second-order stationary points of a primal–dual algorithm model for nonlinear programming

We define a primal–dual algorithm model (second-order Lagrangian algorithm, 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 line search technique that exploits information on the nonconvexity of the augmented Lagrangian function.