{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/solving-constrained-variational-inequalities","title":"Solving Constrained Variational Inequalities via a First-order Interior Point-based Method","arxiv_id":"2206.10575","date":"2022-06-21","proceeding":null,"authors":["Tong Yang","Michael I. Jordan","Tatjana Chavdarova"],"abstract":"We develop an interior-point approach to solve constrained variational inequality (cVI) problems. Inspired by the efficacy of the alternating direction method of multipliers (ADMM) method in the single-objective context, we generalize ADMM to derive a first-order method for cVIs, that we refer to as ADMM-based interior-point method for constrained VIs (ACVI). We provide convergence guarantees for ACVI in two general classes of problems: (i) when the operator is $\\xi$-monotone, and (ii) when it is monotone, some constraints are active and the game is not purely rotational. When the operator is, in addition, L-Lipschitz for the latter case, we match known lower bounds on rates for the gap function of $\\mathcal{O}(1/\\sqrt{K})$ and $\\mathcal{O}(1/K)$ for the last and average iterate, respectively. To the best of our knowledge, this is the first presentation of a first-order interior-point method for the general cVI problem that has a global convergence guarantee. Moreover, unlike previous work in this setting, ACVI provides a means to solve cVIs when the constraints are nontrivial. Empirical analyses demonstrate clear advantages of ACVI over common first-order methods. In particular, (i) cyclical behavior is notably reduced as our methods approach the solution from the analytic center, and (ii) unlike projection-based methods that zigzag when near a constraint, ACVI efficiently handles the constraints.","url_abs":"https://arxiv.org/abs/2206.10575v2","url_pdf":"https://arxiv.org/pdf/2206.10575v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"solving-constrained-variational-inequalities","repo_url":"https://github.com/chavdarova/acvi","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"admm","method_name":"ADMM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.10575","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}