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Optim."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we focus on the nonconvex-strongly-concave minimax optimization problem (MCC), where the inner maximization subproblem contains constraints that couple the primal variable of the outer minimization problem.\u00a0Based on the nondegeneracy of the coupled constraints, we prove that by introducing the dual variable of the inner maximization subproblem, (MCC) has the same first-order minimax points as a nonconvex-strongly-concave minimax optimization problem without coupled constraints (MOL). We then extend our focus to a class of nonconvex-strongly-concave minimax optimization problems (MM) that generalize (MOL). By performing the partial forward-backward envelope to the primal variable of the inner maximization subproblem, we propose a minimization problem (MMPen), where its objective function is explicitly formulated. We prove that the first-order stationary points of (MMPen) coincide with the first-order minimax points of (MM). Therefore, various efficient minimization methods and their convergence guarantees can be directly employed to solve (MM), hence solving (MCC) through (MOL). Preliminary numerical experiments demonstrate the great potential of our proposed approach.<\/jats:p>","DOI":"10.1137\/24m1689727","type":"journal-article","created":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T07:29:35Z","timestamp":1778052575000},"page":"811-840","source":"Crossref","is-referenced-by-count":0,"title":["A Minimization Approach for Minimax Optimization with Coupled Constraints"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4451-2019","authenticated-orcid":true,"given":"Xiaoyin","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Shenzhen University, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7204-8933","authenticated-orcid":true,"given":"Kim-Chuan","family":"Toh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, and Institute of Operations Research and Analytics, National University of Singapore, Singapore 119076."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8962-3794","authenticated-orcid":true,"given":"Shiwei","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Operational Research and Analytics, National University of Singapore, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2725-2633","authenticated-orcid":true,"given":"Nachuan","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Data Science, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,5,6]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1983-0712247-X"},{"key":"ref2","first-page":"1","author":"Bach F.","year":"2024","journal-title":"Math. 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