Constraint Qualification for Generic Parameter Families of Constraints in Optimization
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915531041275904 |
|---|---|
| author | Hamada, Naoki Hayano, Kenta Teramoto, Hiroshi |
| author_facet | Hamada, Naoki Hayano, Kenta Teramoto, Hiroshi |
| contents | Constraint qualifications (CQs) are central to the local analysis of constrained optimization. In this paper, we completely determine the validity of the four classical CQs -- LICQ, MFCQ, ACQ, and GCQ -- for constraint map-germs that arise in generic four-parameter families. Our approach begins by proving that all four CQs are invariant under the action of the group $\mathcal{K}[G]$ and under the operation of reduction. As a consequence, the verification of CQ-validity for a generic constraint reduces to checking CQ-validity on the $\mathcal{K}[G]$-normal forms of fully reduced map-germs. Such normal forms have been classified in our recent work. In the present paper, we verify which CQs hold in each germ appearing in the classification tables from that work. This analysis provides a complete picture of the generic landscape of the four classical CQs. Most notably, we find that there exist numerous generic map-germs for which GCQ holds while all stronger CQs fail, showing that the gap between GCQ and the other qualifications is not an exceptional phenomenon but arises generically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constraint Qualification for Generic Parameter Families of Constraints in Optimization Hamada, Naoki Hayano, Kenta Teramoto, Hiroshi Optimization and Control 57R45 (Primary) 90C25, 90C31, 90C46 (Secondary) Constraint qualifications (CQs) are central to the local analysis of constrained optimization. In this paper, we completely determine the validity of the four classical CQs -- LICQ, MFCQ, ACQ, and GCQ -- for constraint map-germs that arise in generic four-parameter families. Our approach begins by proving that all four CQs are invariant under the action of the group $\mathcal{K}[G]$ and under the operation of reduction. As a consequence, the verification of CQ-validity for a generic constraint reduces to checking CQ-validity on the $\mathcal{K}[G]$-normal forms of fully reduced map-germs. Such normal forms have been classified in our recent work. In the present paper, we verify which CQs hold in each germ appearing in the classification tables from that work. This analysis provides a complete picture of the generic landscape of the four classical CQs. Most notably, we find that there exist numerous generic map-germs for which GCQ holds while all stronger CQs fail, showing that the gap between GCQ and the other qualifications is not an exceptional phenomenon but arises generically. |
| title | Constraint Qualification for Generic Parameter Families of Constraints in Optimization |
| topic | Optimization and Control 57R45 (Primary) 90C25, 90C31, 90C46 (Secondary) |
| url | https://arxiv.org/abs/2510.02381 |