Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem

Abstract

In this paper sufficient second order optimality conditions are established for opti-mal control problems governed by a linear elliptic equation with nonlinear boundary condition, where pointwise constraints on the control are given. The second order condition requires coercivity of the Lagrange function on a suitable subspace together with first order sufficient conditions on a certain set of strongly active points.