Sufficient Optimality in a Parabolic Control Problem

Hans D. Mittelmann
Department of Mathematics
Arizona State University
Box 871804
Tempe, AZ 85287-1804, U.S.A.
mittelmann@asu.edu

Fredi Tröltzsch
Technische Universität Berlin,
Fakultät II - Mathematik und Naturwissenschaften
Sekretariat Ma 4-5, Str. des 17. Juni 136
D-10623 Berlin, Germany
troeltz@math.tu-berlin.de

Abstract: We define a class of parabolic problems with control and state constraints and identify a problem within this class which possesses a locally unique critical point satisfying the second order sufficient optimality conditions. In this solution inequality constraints on the control are strongly active. The second derivative of the Lagrangian is not globally coercive. This is both shown analytically as well as verified numerically for a finite difference discretization.

Key words: Optimal control, nonlinear parabolic equation, second-order sufficient optimality condition, numerical verification