We use limited BFGS updates to approximate the reduced Hessian of the Lagrangian. The linearized state equation and the adjoint equation which are both elliptic partial differential equations are solved using an iterative method. Which leads to inexact step computations in the SQP method.

The optimization problem has been solved
using the ** TRICE_U **
algorithms.

More details are given in the following
slides.
Additional information 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 *

and

M. Heinkenschloss, and L. N. Vicente:
* Analysis of Inexact Trust-Region Interior-Point SQP Algorithms.*