Sequential quadratic programming for certain parameter identification problems

The authors analyze the method of sequential quadratic programming for equality constrained minimization problems in Hilbert spaces of functions, and for the discrete approximations of such problems in the context of an elliptic parameter identification problem. They show how the discretization can be constructed so as to preserve the convergence behavior of the iterates for the infinite dimensional problem in the finite dimensional approximations. The authors use the structure of the parameter identification problem to reduce the size of the linear system for the SQP step and verify nondegeneracy of the constraints.