Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910543060664320 |
|---|---|
| author | Chen, Jiawei Liu, Luyu Lv, Yibing Zhao, Kequan |
| author_facet | Chen, Jiawei Liu, Luyu Lv, Yibing Zhao, Kequan |
| contents | In this paper, we investigate second-order necessary conditions and exact penalty of mathematical programs with switching constraints (MPSC). Some new second-order constraint qualifications and second-order quasi-normality are introduced for (MPSC), which are crucial to establish the second-order necessary conditions and the error bound of (MPSC). We explore the relations among these constraint qualifications in term of (MPSC). The characterizations of Mordukhovich stationary point and strong stationary point of (MPSC) are derived under some mild conditions. A sufficient condition is provided for a Mordukhovich stationary point of (MPSC) being a strong stationary point. The strong second-order necessary conditions as well as weak second-order necessary conditions of (MPSC) are established under these weak constraint qualifications. Finally, we obtain the local exact penalty of (MPSC) under the local error bound or some constraint qualifications in term of (MPSC). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints Chen, Jiawei Liu, Luyu Lv, Yibing Zhao, Kequan Optimization and Control 90C30, 90C33, 90C46 In this paper, we investigate second-order necessary conditions and exact penalty of mathematical programs with switching constraints (MPSC). Some new second-order constraint qualifications and second-order quasi-normality are introduced for (MPSC), which are crucial to establish the second-order necessary conditions and the error bound of (MPSC). We explore the relations among these constraint qualifications in term of (MPSC). The characterizations of Mordukhovich stationary point and strong stationary point of (MPSC) are derived under some mild conditions. A sufficient condition is provided for a Mordukhovich stationary point of (MPSC) being a strong stationary point. The strong second-order necessary conditions as well as weak second-order necessary conditions of (MPSC) are established under these weak constraint qualifications. Finally, we obtain the local exact penalty of (MPSC) under the local error bound or some constraint qualifications in term of (MPSC). |
| title | Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints |
| topic | Optimization and Control 90C30, 90C33, 90C46 |
| url | https://arxiv.org/abs/2407.17285 |