**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

- Introduction
- First and second-order optimality conditions
- The test example
- Numerical Verification
- Bibliography
- About this document ...

2003-01-25