Integration of Sequential Quadratic Programming and Domain Decomposition Methods for Nonlinear Optimal Control Problems

We discuss the integration of a sequential quadratic programming (SQP) method with an optimization-level domain decomposition (DD) preconditioner for the solution of the quadratic optimization subproblems. The DD method is an extension of the well-known Neumann-Neumann method to the optimization context and is based on a decomposition of the first order system of optimality conditions. The SQP method uses a trust-region globalization and requires the solution of quadratic subproblems that are known to be convex, hence solving the first order system of optimality conditions associated with these subproblems is equivalent to solving these subproblems. In addition, our SQP method allows the inexact solution of these subproblems and adjusts the level of exactness with which these subproblems are solved based on the progress of the SQP method. The overall method is applied to a boundary control problem governed by a semilinear elliptic equation.