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math.OC2021★ 3 cited
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the cod…
math.OC2021★ 4 cited
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Maurício Silva Louzeiro, Ronny Bergmann, Roland Herzog
In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience…