Optimal Control of the Stationary Navier–Stokes Equations with Mixed Control‐State Constraints

Abstract

In this paper we consider the distributed optimal control of the Navier–Stokes equations in the presence of pointwise mixed control‐state constraints. After deriving a first order necessary condition, the regularity of the mixed constraint multiplier is investigated. Second order sufficient optimality conditions are studied as well. In the last part of the paper, a semismooth Newton method is applied for the numerical solution of the control problem. The convergence of the method is proved and numerical experiments are carried out.