Optimization techniques for solving elliptic control problems with controland state constraints. Part 2: Distributed control

Part 2 continues the study of optimization techniques for elliptic control problems subject to control and state constraints and is devoted to distrib uted control. Boundary conditions are of mixed Dirichlet and Neumann type. Necessary conditions of optimality are formally stated in form of a local P ontryagin minimum principle, By introducing suitable discretization schemes , the control problem is transcribed into a nonlinear programming problem. The problems are formulated as AMPL (R. Fourer, D.M. Gay, and B.W. Kernigha n, "AMPL: A modeling Language for Mathematical Programming", Duxbury Press, Brooks-Cole Publishing Company, 1993) scripts and several optimization cod es are applied. In particular it is shown that a recently developed interio r point method is able to solve theses problems even for high discretizatio ns. Several numerical examples with Dirichlet and Neumann boundary conditio ns are provided that illustrate the performance of the algorithm for differ ent types of controls including bang-bang controls, The necessary condition s of optimality are checked numerically in the presence of active control a nd state constraints.