{"ID":2856623,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.12007","arxiv_id":"2510.12007","title":"Semi-infinite Nonconvex Constrained Min-Max Optimization","abstract":"Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this paper, we investigate a class of nonconvex min-max optimization problems with nonconvex infinite constraints, motivated by applications such as adversarial robustness and safety-constrained learning. We propose a novel inexact dynamic barrier primal-dual algorithm and establish its convergence properties. Specifically, under the assumption that the squared infeasibility residual function satisfies the Lojasiewicz inequality with exponent $θ\\in (0,1)$, we prove that the proposed method achieves $\\mathcal{O}(ε^{-3})$, $\\mathcal{O}(ε^{-6θ})$, and $\\mathcal{O}(ε^{-3θ/(1-θ)})$ iteration complexities to achieve an $ε$-approximate stationarity, infeasibility, and complementarity slackness, respectively. Numerical experiments on robust multitask learning with task priority further illustrate the practical effectiveness of the algorithm.","short_abstract":"Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this paper, we investigate a class of nonconvex min-max optimization problems with noncon...","url_abs":"https://arxiv.org/abs/2510.12007","url_pdf":"https://arxiv.org/pdf/2510.12007v1","authors":"[\"Cody Melcher\",\"Zeinab Alizadeh\",\"Lindsey Hiett\",\"Afrooz Jalilzadeh\",\"Erfan Yazdandoost Hamedani\"]","published":"2025-10-13T22:59:34Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}