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.