424. Proximal splitting algorithms in nonlinear spaces
Invited abstract in session TC-5: Randomized Optimization algorithms II, stream Optimization for machine learning.
Tuesday, 14:00-16:00Room: B100/4013
Authors (first author is the speaker)
| 1. | Russell Luke
|
| Institute for Numerical and Applied Math, Universität Göttingen |
Abstract
In the setting of CAT(????) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces. This is specialized to the computation of Frechet means in nonlinear spaces using deterministic and radomized methods.
Keywords
- First-order optimization
- Computational mathematical optimization
- Non-smooth optimization
Status: accepted
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