{"ID":2826742,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.18330","arxiv_id":"2512.18330","title":"Learning Generalized Nash Equilibria in Non-Monotone Games with Quadratic Costs","abstract":"We study generalized Nash equilibrium (GNE) problems in games with quadratic costs and individual linear equality constraints. Departing from approaches that require strong monotonicity and/or shared constraints, we reformulate the KKT conditions of the (generally non-monotone) games into a tractable convex program whose objective satisfies the Polyak-Lojasiewicz (PL) condition. This PL geometry enables a distributed gradient method over a fixed communication graph with global geometric (linear) convergence to a GNE. When gradient information is unavailable or costly, we further develop a zero-order fully distributed scheme in which each player uses only local cost evaluations and their own constraint residuals. With an appropriate step size policy, the proposed zero-order method converges to a GNE, provided one exists, at rate O(1/t).","short_abstract":"We study generalized Nash equilibrium (GNE) problems in games with quadratic costs and individual linear equality constraints. Departing from approaches that require strong monotonicity and/or shared constraints, we reformulate the KKT conditions of the (generally non-monotone) games into a tractable convex program who...","url_abs":"https://arxiv.org/abs/2512.18330","url_pdf":"https://arxiv.org/pdf/2512.18330v1","authors":"[\"Tatiana Tatarenko\",\"Lucas Wey Hacker\"]","published":"2025-12-20T11:54:53Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}