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When combining the numerical concept of variational discretization andsemi-smooth Newton methods for the numerical solution of pde constrainedoptimization with control constraints, special emphasis has to be taken on theimplementation, convergence and globalization of the numerical algorithm. Inthe present work we address all these issues. In particular we prove fast localconvergence of the algorithm and propose two different globalization strategieswhich are applicable in many practically relevant mathematical settings. Weillustrate our analytical and algorithmical findings by numerical experiments.

Variational discretization and semi-smooth Newton methods;  implementation, convergence and globalization in pde constrained optimization  with control constraints