Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910596434231296 |
|---|---|
| author | Dolgopolik, M. V. |
| author_facet | Dolgopolik, M. V. |
| contents | In this article, we present new general results on existence of augmented Lagrange multipliers. We define a penalty function associated with an augmented Lagrangian, and prove that, under a certain growth assumption on the augmenting function, an augmented Lagrange multiplier exists if and only if this penalty function is exact. We also develop a new general approach to the study of augmented Lagrange multipliers called the localization principle. The localization principle allows one to study the local behaviour of the augmented Lagrangian near globally optimal solutions of the initial optimization problem in order to prove the existence of augmented Lagrange multipliers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_03046 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle Dolgopolik, M. V. Optimization and Control 90C30, 65K05 In this article, we present new general results on existence of augmented Lagrange multipliers. We define a penalty function associated with an augmented Lagrangian, and prove that, under a certain growth assumption on the augmenting function, an augmented Lagrange multiplier exists if and only if this penalty function is exact. We also develop a new general approach to the study of augmented Lagrange multipliers called the localization principle. The localization principle allows one to study the local behaviour of the augmented Lagrangian near globally optimal solutions of the initial optimization problem in order to prove the existence of augmented Lagrange multipliers. |
| title | Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle |
| topic | Optimization and Control 90C30, 65K05 |
| url | https://arxiv.org/abs/1802.03046 |