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2810. The Riemannian Convex Bundle Method
Invited abstract in session TB-41: Optimization on Manifolds, stream Optimization on Geodesic Metric Spaces: Smooth and Nonsmooth.
Tuesday, 10:30-12:00Room: 97 (building: 306)
Authors (first author is the speaker)
| 1. | Hajg Jasa
|
| Department of Mathematical Sciences (IMF), Norwegian University of Science and Technology (NTNU) | |
| 2. | Ronny Bergmann
|
| Department of Mathematical Sciences, Norwegian University of Science and Technology | |
| 3. | Roland Herzog
|
| Interdisciplinary Center for Scientific Computing |
Abstract
Within the context of optimization on manifolds, a research direction of particular interest is the investigation of algorithms fit to optimize non-smooth objectives. This research area is relevant since the need for optimizing non-smooth objective functions arises in many real-world problems and applications such as image and signal restoration, denoising, inpainting, etc. In this talk, we introduce the convex bundle method to solve convex, nonsmooth optimization problems on Riemannian manifolds. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallely transported into the current serious iterate. This approach generalizes the dual form of classical bundle subproblems in Euclidean space. Several numerical examples implemented using the Julia package Manopt.jl illustrate the performance of the proposed method and compare it to other non-smooth optimization algorithms.
Keywords
- Non-smooth Optimization
- Algorithms
- Convex Optimization
Status: accepted
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