On the numerical solution of elliptic and parabolic optimal control problems

This paper regards the solution of some optimal control problems, transcribed as constrained optimization problems, with the main purpose of analysing how the solution changes when the number of discretization points is modified. The problems studied, which include both boundary and distributed elliptic optimal control problems as well as parabolic control problems, have in fact been written in AMPL language and solved by changing the size of the discretization mesh, so to analyse the variance of the minimum of the objective as the number of discretization points increases. Moreover, the problems have been solved using different solvers (such as MINOS, LOQO, IPOPT, SNOPT and KNITRO) and different kinds of discretization so to consider the influence of these parameters on the final results.