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Daily Overview |
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Pl 5: Plenary Lecture
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| Presentations | ||
Semismooth Newton Methods in Infinite Dimensions: Foundations, Recent Advances, and Applications Technical University of Munich, Germany
Newton’s method remains a cornerstone of numerical analysis, yet the classical reliance on
continuous differentiability restricts its applicability. Identifying minimal conditions that still
guarantee superlinear convergence leads to the notion of Newton differentiability. While it admits
a clean abstract formulation, verifying Newton differentiability for concrete nonsmooth operators
in infinite-dimensional spaces—such as Nemytskii operators, projections onto closed convex sets,
or solution maps of variational inequalities—can require substantial analytical work; nevertheless,
it has been established for broad, practically relevant classes of such operators.
The resulting semismooth Newton methods enable the efficient solution of nonsmooth operator
equations and variational problems. Combined with proximal or augmented Lagrangian techniques, they extend to nonsmooth minimization, further broadening their scope.
The talk focuses on infinite-dimensional settings, as encountered in PDE-constrained optimization. It traces the development of the theory from its foundations to recent advances. Selected applications illustrate the versatility and computational efficiency of the approach
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