Fenchel Duality and a Separation Theorem on Hadamard Manifolds

  title={Fenchel Duality and a Separation Theorem on Hadamard Manifolds},
  author={Ronny Bergmann and Roland Herzog and M. S. Louzeiro},
  journal={SIAM Journal on Optimization},
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 that the conjugate depends on the choice of a certain point on the manifold, as previous definitions required. On the other hand, this new definition still possesses properties known to hold in the Euclidean case. It even yields a broader interpretation of the Fenchel conjugate in the Euclidean case itself. Most… 
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