44. Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems
Invited abstract in session TB-6: Advances in nonsmooth optimization, stream Nonsmooth and nonconvex optimization.
Tuesday, 10:30-12:30Room: B100/7013
Authors (first author is the speaker)
| 1. | Yassine Nabou
|
| Department of Mathematics and Statistics, University of Helsinki | |
| 2. | Lahcen EL BOURKHISSI
|
| Department of Automatic Control and Systems Engineering, University POLITEHNICA of Bucharest | |
| 3. | Sebastian Stich
|
| CISPA Helmholtz Center for Information Security | |
| 4. | Tuomo Valkonen
|
| Escuela Politécnica Nacional |
Abstract
In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a Linearized Block Coordinate Descent method for solving composite optimization problems. At each iteration, a random block is selected, and the smooth components of the objective are linearized along the chosen block in a Gauss-Newton approach. For the monotone variant, we establish a global sublinear convergence rate to a stationary point under the assumption of bounded iterates. For the nonmonotone variant, we derive a global sublinear convergence rate without requiring global Lipschitz continuity or bounded iterates. Preliminary numerical experiments on logistic regression highlight the promising performance of the proposed approach.
Keywords
- Non-smooth optimization
- Large-scale optimization
- First-order optimization
Status: accepted
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