7. Horospherically Convex Optimization on Hadamard Manifolds
Invited abstract in session FD-2: Deterministic and stochastic optimization beyond Euclidean geometry, stream Advances in first-order optimization.
Friday, 14:10 - 15:50Room: M:O
Authors (first author is the speaker)
| 1. | Christopher Criscitiello
|
| Mathematics, EPFL | |
| 2. | Jungbin Kim
|
| Seoul National University |
Abstract
Many Euclidean notions, like affine functions, do not generalize well within the framework of geodesic convexity. Using Busemann functions as a building block, we introduce an alternative generalization of convexity to Hadamard manifolds called horospherical convexity (h-convexity). We provide algorithms for h-convex optimization which have rates *exactly* matching those from Euclidean space (including full acceleration). As a consequence, we obtain the best known rates for the minimal enclosing ball problem. We also establish necessary and sufficient conditions for h-convex interpolation.
Keywords
- Complexity and efficiency of optimization algorithms
- Linear and nonlinear optimization
- Convex and non-smooth optimization
Status: accepted
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