Sufficient Optimality for Discretized Parabolic
and Elliptic Control Problems
Hans D. Mittelmann
Department of Mathematics
Arizona State University
Tempe, AZ 85287-1804, U.S.A.
We study optimal control problems for semilinear parabolic and elliptic
equations subject to control and state constraints. We quote known
second-order sufficient optimality conditions (SSC) from the literature.
Both problem classes are discretized by a
finite difference method. The discrete SSC are stated and numerically
verified for fine discretizations with the help of sparse linear algebra
techniques. This confirms initial results reported earlier for such
discretized control problems. In order to relate these results to
optimality for the underlying continuous problems corresponding
theoretical, especially convergence, results are still unavailable at