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Control Optim."],"published-print":{"date-parts":[[2024,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we propose consensus-based optimization for saddle point problems (CBO-SP), a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of swarm intelligence, the method employs two groups of interacting particles, one which performs a minimization over one variable while the other performs a maximization over the other variable. The two groups constantly exchange information through a suitably weighted average. This paradigm permits a passage to the mean-field limit, which makes the method amenable to theoretical analysis, and it allows to obtain rigorous convergence guarantees under reasonable assumptions about the initialization and the objective function, which most notably include nonconvex-nonconcave objectives. We further provide numerical evidence for the success of the algorithm.<\/jats:p>","DOI":"10.1137\/22m1543367","type":"journal-article","created":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T10:45:30Z","timestamp":1711363530000},"page":"1093-1121","source":"Crossref","is-referenced-by-count":18,"title":["Consensus-Based Optimization for Saddle Point Problems"],"prefix":"10.1137","volume":"62","author":[{"given":"Hui","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinniao","family":"Qiu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Calgary, T2N 1N4 Calgary, Canada."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Konstantin","family":"Riedl","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany."},{"name":"Munich Center for Machine Learning, 80593 Munich, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,3,25]]},"reference":[{"key":"ref1","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold L.","year":"1974"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"G. 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