Convergence to second order stationary points in inequality constrained optimization

We propose a new algorithm for the nonlinear inequality constrained minimiz ation problem, and prove that it generates a sequence converging to points satisfying the KKT second order necessary conditions for optimality. The al gorithm is a line search algorithm using directions of negative curvature a nd it can be viewed as a nontrivial extension of corresponding known techni ques from unconstrained to constrained problems. The main tools employed in the definition and in the analysis of the algorithm are a differentiable e xact penalty function and results from the theory of LC1 functions.