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Description: |
We focus on the primal-dual active set strategy, a versatile algorithmic tool in solving constrained optimal control problems, obstacle problems or, more generally, (linear) complementarity problems in function space settings. After reviewing its motivation by Moreau-Yosida type approximations, discussing some of its main properties and conditional global convergence results, we establish the equivalence of the primal dual active set strategy to semi-smooth Newton methods in function spaces. This latter aspect relies on a suitable generalization of the differential calculus (i.e. slant differentiability) for non-smooth operators to infinite dimensions and offers a different view on local convergence properties, like locally superlinear convergence rates, well known from semi-smooth Newton methods in finite dimensions. Under appropriate growth conditions one is able to establish ``convergence-with-a-rate'' results. Also, the connection to Newton type methods in function spaces allows to prove the important property of mesh independence of semi-smooth Newton methods for operator equations in general, and the primal-dual active set strategy in particular. Finally, numerical results shall emphasize our theoretical findings.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Michael Hintermuller (University of Graz, Áustria)
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Place: |
Room 5.5
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| Research Groups: |
-Numerical Analysis and Optimization
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See more:
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