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No-gap second-order conditions for minimization problems in spaces of measures
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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.
Forward citations
Cited by 2 Pith papers
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No-gap second-order conditions for optimization problems involving transport distances
No-gap second-order conditions for transport-regularized measure optimization are equivalent to quadratic growth once the Kantorovich potential satisfies a quadratic-growth regularity assumption.
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