We consider an optimal control problem which is related to the heating of a probe in a kiln. The goal is to control the heating process in such a way that the temperature inside the probe follows a certain desired temperature profile.

The optimization problem has been solved using the TRICE_U algorithms.
The linearized state equation and the adjoint equation which are both discretized linear parabolic partial differential equations are solved either directly of using an iterative method. The latter leads to inexact step computations in the SQP method. The effects of the inexact steps are studied numerically.

Additional information and more numerical tests can be found in the papers
J. E. Dennis, M. Heinkenschloss, and L. N. Vicente: Trust-Region Interior-Point SQP Algorithms for a Class of Nonlinear Programming Problems
M. Heinkenschloss, and L. N. Vicente: Analysis of Inexact Trust-Region Interior-Point SQP Algorithms.