| Full text | |
| Author(s): |
Atenas, Felipe
;
Sagastiz, Claudia
;
Silva, Paulo J. S.
;
Solodov, Mikhail
Total Authors: 4
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON OPTIMIZATION; v. 33, n. 1, p. 27-pg., 2023-01-01. |
| Abstract | |
We present a framework for analyzing convergence and local rates of convergence of a class of descent algorithms, assuming the objective function is weakly convex. The framework is general, in the sense that it combines the possibility of explicit iterations (based on the gradient or a subgradient at the current iterate), implicit iterations (using a subgradient at the next iteration, like in the proximal schemes), as well as iterations when the associated subgradient is specially constructed and does not correspond either to the current or the next point (this is the case of descent steps in bundle methods). Under the subdifferential-based error bound on the distance to critical points, linear rates of convergence are established. Our analysis applies, among other techniques, to prox-descent for decomposable functions, the proximal-gradient method for a sum of functions, redistributed bundle methods, and a class of algorithms that can be cast in the feasible descent framework for constrained optimization. (AU) | |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 19/20023-1 - Sthochastic variational analysis applied to the energy industry |
| Grantee: | Felipe Eduardo Atenas Maldonado |
| Support Opportunities: | Scholarships in Brazil - Doctorate |