Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems

Authors:
Hans D. Mittelmann
Affiliations:
Arizona State University, Department of Mathematics, Tempe, Arizona 85287-1804, USA. mittelmann@asu.edu
Venue:
Computational Optimization and Applications
Year:
2001

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Abstract

We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method. The discrete SSC are stated and numerically verified in all cases providing an indication of optimality where only necessary conditions had been studied before.