A smoothed penalty iteration for state constrained optimal control problems for partial differential equations

Abstract

We consider general, not necessarily convex, optimization problems with inequality constraints. We show that the smoothed penalty algorithm generates a sequence that converges to a stationary point. In particular, we show that the algorithm provides approximations of the multipliers for the inequality constraints. The theoretical analysis is illustrated by numerical examples for optimal control problems with pointwise state constraints and Robin boundary conditions as presented by Grossmann, Kunz, and Meischner [C. Grossmann, H. Kunz, and R. Meischner, Elliptic control by penalty techniques with control reduction, in IFIP Advances in Information and Communication Technology, Springer-Verlag, Berlin Heidelberg, 2009, pp. 251–267].