Extragradient methods with complexity guarantees for hierarchical variational inequalities
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912845005848576 |
|---|---|
| author | Dvurechensky, Pavel Marschner, Meggie Shtern, Shimrit Staudigl, Mathias |
| author_facet | Dvurechensky, Pavel Marschner, Meggie Shtern, Shimrit Staudigl, Mathias |
| contents | In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under equilibrium constraints, constrained min-max problems, hierarchical game problems, optimal control under VI constraints, and simple bilevel optimization problems. For this general problem formulation, we establish rates of convergence in terms of suitably constructed gap functions, measuring feasibility gaps and optimality gaps. We present worst-case iteration complexity results on both levels of the variational problem, as well as weak convergence under a geometric weak sharpness condition on the lower level solution set. Our results match and improve the state of the art in terms of their iteration complexity and the generality of the problem formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20791 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extragradient methods with complexity guarantees for hierarchical variational inequalities Dvurechensky, Pavel Marschner, Meggie Shtern, Shimrit Staudigl, Mathias Optimization and Control Systems and Control 65K15, 90C33, 49M29 In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under equilibrium constraints, constrained min-max problems, hierarchical game problems, optimal control under VI constraints, and simple bilevel optimization problems. For this general problem formulation, we establish rates of convergence in terms of suitably constructed gap functions, measuring feasibility gaps and optimality gaps. We present worst-case iteration complexity results on both levels of the variational problem, as well as weak convergence under a geometric weak sharpness condition on the lower level solution set. Our results match and improve the state of the art in terms of their iteration complexity and the generality of the problem formulation. |
| title | Extragradient methods with complexity guarantees for hierarchical variational inequalities |
| topic | Optimization and Control Systems and Control 65K15, 90C33, 49M29 |
| url | https://arxiv.org/abs/2512.20791 |