Quadratic convergence of an SQP method for some optimization problems with applications to control theory

We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an L² neighborhood of a local solution that satisfies no-gap second-order sufficient optimality conditions and a strict complementarity condition, we obtain stability and quadratic convergence in Lq for all q, where p 2 depends on the problem. Many of the usual optimal control problems of partial differential equations fit into this abstract formulation. Some examples are given in the paper. Finally, a computational comparison with other versions of the SQP method is presented.