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

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.

💡 Research Summary

The paper addresses the solution of strongly convex optimal control problems in Hilbert spaces by developing a globally convergent, inexact semismooth Newton method applied to the dual formulation. Starting from the primal problem
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