2025/03/27 by Wachsmuth, Daniel · 2 citations
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2503.21612
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.