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Exact penalization of pointwise constraints for optimal control problems

Casas E.

Control and Cybernetics

2009

Vol. 38, no 4A

1131-1150

In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.

Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations

Roubicek T., Troltzsch F.

Control and Cybernetics

2003

Vol. 32, no 3

683-705

An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.