A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910808534941696 |
|---|---|
| author | López-Rivera, Sergio Pérez-Aros, Pedro Vilches, Emilio |
| author_facet | López-Rivera, Sergio Pérez-Aros, Pedro Vilches, Emilio |
| contents | In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we propose a projected variable smoothing algorithm and establish a complexity bound of $\mathcal{O}(ε^{-3})$ to achieve an $ε$-approximate solution. Second, we investigate the Moreau envelope and the proximity operator of functions defined as the supremum of weakly convex functions, and we compute the proximity operator in two important cases. In addition, we apply the proposed algorithm for solving a distributionally robust optimization problem, the LASSO with linear constraints, and the max dispersion problem. We illustrate numerical results for the max dispersion problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions López-Rivera, Sergio Pérez-Aros, Pedro Vilches, Emilio Optimization and Control 90C2, 49J52, 65K05 In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we propose a projected variable smoothing algorithm and establish a complexity bound of $\mathcal{O}(ε^{-3})$ to achieve an $ε$-approximate solution. Second, we investigate the Moreau envelope and the proximity operator of functions defined as the supremum of weakly convex functions, and we compute the proximity operator in two important cases. In addition, we apply the proposed algorithm for solving a distributionally robust optimization problem, the LASSO with linear constraints, and the max dispersion problem. We illustrate numerical results for the max dispersion problem. |
| title | A Projected Variable Smoothing for Weakly Convex Optimization and Supremum Functions |
| topic | Optimization and Control 90C2, 49J52, 65K05 |
| url | https://arxiv.org/abs/2502.00525 |