Fenchel Duality Theory and a Primal-Dual Algorithm on Riemannian Manifolds

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• Ronny Bergmann (TU Chemnitz, Germany)
• Wednesday 26 February 2020, 12:00-13:00
• Physics West 103.

If you have a question about this talk, please contact Sergey Sergeev.

In this talk we introduces a new duality theory that generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its properties, e.g., the Fenchel–Young inequality and the characterization of the convex subdifferential using the analogue of the Fenchel—Moreau Theorem. These properties of the Fenchel conjugate are employed to derive a Riemannian primal-dual optimization algorithm, and to prove its convergence for the case of Hadamard manifolds under appropriate assumptions. Numerical results illustrate the performance of the algorithm, which competes with the recently derived Douglas–Rachford algorithm on manifolds of nonpositive curvature. Furthermore we show numerically that our novel algorithm even converges on manifolds of positive curvature.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

This talk is included in these lists:

• Optimisation and Numerical Analysis Seminars
• Physics West 103
• School of Mathematics Events

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