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

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

2009-12-02

arxiv.org/abs/0912.0488v1

Mathematics

Optimization and Control

Scientific paper

When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation, convergence and globalization of the numerical algorithm. In the present work we address all these issues. In particular we prove fast local convergence of the algorithm and propose two different globalization strategies which are applicable in many practically relevant mathematical settings. We illustrate our analytical and algorithmical findings by numerical experiments.

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