Second-Order Optimality Conditions in Nonlinear Programming Obtained by Way of Epi-Derivatives

Dedicated to the memory of Robin W. Chaney Second-order optimality conditions for finite-dimensional smooth and nonsmooth nonlinear programming are obtained by a new method that emphasizes a close connection with geometrical approximation of the essential objective function. The approximation is secured by the use of certain epi-derivatives defined by epiconvergence. The optimality conditions are expressed in a form that covers general interval constraints and their possible representation through penalties or an augmented Lagrangian. An abstract constraint involving restriction to a convex polyhedron is incorporated.