{"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/a-primal-dual-assisted-penalty-approach-to","title":"A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints","arxiv_id":"2406.10148","date":"2024-06-14","proceeding":null,"authors":["Liuyuan Jiang","Quan Xiao","Victor M. Tenorio","Fernando Real-Rojas","Antonio G. Marques","Tianyi Chen"],"abstract":"Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. 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