On the Lagrange-Newton-SQP method for the optimal control of semilinear parabolic equations

A class of Lagrange-Newton-SQP methods is investigated for optimal control problems governed by semilinear parabolic initial-boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality conditio n for the reference solution, local quadratic convergence is proved. The pr oof is based on the theory of Newton methods for generalized equations in B anach spaces.