Numerical Solution of Parabolic State Constrained Control Problems Using SQP- and Interior-Point-Methods

In this paper we consider the problem to fire ceramic kilns according to a given predetermined reference profile. It can be written as an optimal control problem with a nonlinear parabolic differential equation and control input through the boundary. The objective is a quadratic performance criterion for the observed temperature inside the probe and the firing curve. In addition, restrictions on the maximal temperature are imposed which leads to state constraints. The discretization of this problem gives an optimization problem with equality and inequality constraints. The numerical solution of this problem is carried out with a SQP-method where the quadratic subproblems are solved by an interior point algorithm. The goal of this paper is not to obtain theoretical results but to investigate if these type of methods can be used in the numerical solution of parabolic control problems.