Preprint 35-2005

On optimal control problems with convex control constraints

Author(s) : Daniel Wachsmuth

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 35-2005

MSC 2000

49M05 Methods based on necessary conditions

26E25 Set-valued functions

49K20 Problems involving partial differential equations

Abstract :
We investigate optimal control problems with vector-valued controls. As model problem serve the optimal distributed control of the instationary Navier-Stokes equations. We study pointwise convex control constraints, which is a constraint of the form u(x,t)?U(x,t) that has to hold on the domain Q. Here, U is an set-valued mapping that is assumed to be measurable with convex and closed images. We establish first-order necessary as well as second-order sufficient optimality conditions. And we prove regularity results for locally optimal controls.

Keywords : Optimal control, convex control constraints, set-valued mappings, active-set strategy, Navier-Stokes equations