An Extension of Pontryagin’s Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities

This paper deals with state-constrained optimal control problems governed by semi-linear elliptic equations or variational inequalities. By using Ekeland’s principle, a minimum principle of Pontryagin’s type under some stability conditions of the optimal cost with respect to the state constraints is derived.