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arXiv · 2503.21612

A globalized inexact semismooth Newton method for strongly convex optimal control problems

Daniel Wachsmuth
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Abstract

We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable objective. We prove global strong convergence of iterates as well as transition to local superlinear convergence. The latter needs a second-order Taylor expansion involving semismooth derivative concepts. The convergence of the globalized method is demonstrated in numerical examples, for which the local unglobalized method diverges.

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Daniel Wachsmuth. 2025-03-27. A globalized inexact semismooth Newton method for strongly convex optimal control problems. https://doi.org/10.46298/jnsao-2026-15574

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