Tuomo Valkonen

Our work “Forward–backward splitting in bilaterally bounded Alexandrov spaces” with Heikki von Koch, has been stamped by COAP.

https://rdcu.be/fl3o5

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#optimization #manifold

Forward–backward splitting in bilaterally bounded Alexandrov spaces

Jun 2 at 12:05pmWeb
Show threadTuomo ValkonenJun 2

Abstract:

With the goal of solving optimisation problems on non-Riemannian manifolds, such as geometrical surfaces with sharp edges, we develop and prove the convergence of a forward–backward method in Alexandrov spaces with curvature bounded both from above and from below.
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Show threadTuomo ValkonenJun 2
This bilateral boundedness is crucial for the availability of both the gradient and proximal steps, instead of just one or the other. We numerically demonstrate the behaviour of the proposed method on simple geometrical surfaces in ℝ³.