Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints
Based on some tools of variation analysis, we deal with first- and second-order necessary optimality conditions for a class of optimal control problems governed by semilinear elliptic equations and stationary NavierStokes equations with pure state constraints. To do this, we first derive optimality conditions for an abstract optimal control problem and then apply the obtained results to derive second-order necessary optimality conditions for semilinear elliptic optimal control problems as well as optimal control problems governed by stationary NavierStokes equations.
second-order necessary optimality condition pure state constraint semilinear elliptic equation stationary navierstokes equation regularity condition 49k20 35j25