Abstract: We analyze a sequential quadratic programming (SQP) 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 E [p, infinito] 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.

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