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Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player\u2019s constraints are linear in their own strategy. For such GNEPs, the KKT sets can be represented as unions of simpler sets by Carath\u00e9odory\u2019s theorem. We give a convenient representation for KKT sets using partial Lagrange multiplier expressions. This produces a set of branch polynomial optimization problems, which can be efficiently solved by Moment-SOS relaxations. By doing this, we can compute all generalized Nash equilibria or detect their nonexistence. This method may not be very scalable to large-scale GNEPs. Numerical experiments are provided to demonstrate the computational efficiency.<\/jats:p>","DOI":"10.1137\/24m1699395","type":"journal-article","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T07:00:36Z","timestamp":1785308436000},"page":"1589-1618","source":"Crossref","is-referenced-by-count":0,"title":["Generalized Nash Equilibrium Problems with Quasi-linear Constraints"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7908-3440","authenticated-orcid":true,"given":"Jiyoung","family":"Choi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California San Diego, La Jolla, CA 92093 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiawang","family":"Nie","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California San Diego, La Jolla, CA 92093 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4951-768X","authenticated-orcid":true,"given":"Xindong","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6658-151X","authenticated-orcid":true,"given":"Suhan","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China, 200240."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,29]]},"reference":[{"key":"ref1","unstructured":"M. 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