The numerical solution of inverse problems often leads to
large-scale optimization problems.
In this talk we discuss the solution of such problems
using sequential quadratic programming (SQP) methods.
While SQP methods are well established and successfully
used for constrained optimization, there are still open
issues when SQP subproblems, in particular the linearized
constraints, are not solved by direct linear algebra but
by iterative methods. Critical issues are the control of inexactness
to achieve global convergence of the SQP method and the design
of preconditioners for the solution of saddle point SQP subproblems.
In this talk we will first provide the necessary background on SQP methods and motivate the issues that arise when SQP subproblems are solved iteratively. Then we will propose ways to control inexactness to maintain global and local convergence, and we will discuss the construction of preconditioners for the saddle point SQP subproblems. Theoretical results will be supported by applications to inverse problem testexamples.