No-gap second-order conditions for minimization problems in spaces of measures
- Resource Type
- Working Paper
- Authors
- Wachsmuth, Gerd; Walter, Daniel
- Source
- Subject
- Mathematics - Optimization and Control
46E27, 49K27, 49J52, 49J53
- Language
Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical analysis is played by the assumption that the optimal dual state admits finitely many global extrema and satisfies a second-order sufficient optimality condition in each one of them. In this work, we show the full equivalence of these structural assumptions to a no-gap second-order condition involving the second subderivative of the Radon norm as well as to a local quadratic growth property of the objective functional with respect to the bounded Lipschitz norm.