Convergence to Second Order Stationary Points in Inequality Constrained Optimization

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