Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2310.07922 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911836865036288 |
|---|---|
| author | Devanathan, Nikhil Boyd, Stephen |
| author_facet | Devanathan, Nikhil Boyd, Stephen |
| contents | In 1963 Boris Polyak suggested a particular step size for gradient descent methods, now known as the Polyak step size, that he later adapted to subgradient methods. The Polyak step size requires knowledge of the optimal value of the minimization problem, which is a strong assumption but one that holds for several important problems. In this paper we extend Polyak's method to handle constraints and, as a generalization of subgradients, general minorants, which are convex functions that tightly lower bound the objective and constraint functions. We refer to this algorithm as the Polyak Minorant Method (PMM). It is closely related to cutting-plane and bundle methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07922 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polyak Minorant Method for Convex Optimization Devanathan, Nikhil Boyd, Stephen Optimization and Control In 1963 Boris Polyak suggested a particular step size for gradient descent methods, now known as the Polyak step size, that he later adapted to subgradient methods. The Polyak step size requires knowledge of the optimal value of the minimization problem, which is a strong assumption but one that holds for several important problems. In this paper we extend Polyak's method to handle constraints and, as a generalization of subgradients, general minorants, which are convex functions that tightly lower bound the objective and constraint functions. We refer to this algorithm as the Polyak Minorant Method (PMM). It is closely related to cutting-plane and bundle methods. |
| title | Polyak Minorant Method for Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2310.07922 |