{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T09:20:38Z","timestamp":1790673638215,"version":"4.1.0"},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T00:00:00Z","timestamp":1697155200000},"content-version":"am","delay-in-days":316,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"},{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T00:00:00Z","timestamp":1669852800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["CSC202006010086"],"award-info":[{"award-number":["CSC202006010086"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1016\/j.neunet.2022.09.014","type":"journal-article","created":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T03:24:59Z","timestamp":1663903499000},"page":"49-57","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":12,"special_numbering":"C","title":["MG-CNN: A deep CNN to predict saddle points of matrix games"],"prefix":"10.1016","volume":"156","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6450-9365","authenticated-orcid":false,"given":"Dawen","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdel","family":"Lisser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.neunet.2022.09.014_b1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40537-021-00444-8","article-title":"Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions","volume":"8","author":"Alzubaidi","year":"2021","journal-title":"Journal of Big Data"},{"key":"10.1016\/j.neunet.2022.09.014_b2","series-title":"Introduction to linear optimization, volume 6","author":"Bertsimas","year":"1997"},{"key":"10.1016\/j.neunet.2022.09.014_b3","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1007\/s10957-016-0892-3","article-title":"Operator splitting for conic optimization via homogeneous self-dual embedding","volume":"169","author":"Brendan","year":"2016","journal-title":"Journal of Optimization Theory and Applications"},{"key":"10.1016\/j.neunet.2022.09.014_b4","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.ejor.2015.12.024","article-title":"Random-payoff two-person zero-sum game with joint chance constraints","volume":"252","author":"Cheng","year":"2016","journal-title":"European Journal of Operational Research"},{"key":"10.1016\/j.neunet.2022.09.014_b5","first-page":"1","article-title":"Deep learning","volume":"29","author":"Courville","year":"2016","journal-title":"Nature"},{"key":"10.1016\/j.neunet.2022.09.014_b6","series-title":"Linear programming and extensions","author":"Dantzig","year":"1963"},{"key":"10.1016\/j.neunet.2022.09.014_b7","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1609\/aimag.v40i2.2847","article-title":"A survey of game theoretic approaches for adversarial machine learning in cybersecurity tasks","volume":"40","author":"Dasgupta","year":"2019","journal-title":"AI Magazine"},{"key":"10.1016\/j.neunet.2022.09.014_b8","article-title":"BERT: pre-training of deep bidirectional transformers for language understanding","author":"Devlin","year":"2018","journal-title":"CoRR"},{"key":"10.1016\/j.neunet.2022.09.014_b9","first-page":"1","article-title":"CVXPY: A Python-embedded modeling language for convex optimization","volume":"17","author":"Diamond","year":"2016","journal-title":"Journal of Machine Learning Research"},{"key":"10.1016\/j.neunet.2022.09.014_b10","series-title":"Investment under uncertainty","first-page":"1","author":"Dixit","year":"2012"},{"key":"10.1016\/j.neunet.2022.09.014_b11","series-title":"2013 European control conference","first-page":"3071","article-title":"ECOS: An SOCP solver for embedded systems","author":"Domahidi","year":"2013"},{"key":"10.1016\/j.neunet.2022.09.014_b12","series-title":"Game theory","author":"Fudenberg","year":"1991"},{"key":"10.1016\/j.neunet.2022.09.014_b13","series-title":"GNU linear programming kit","author":"GLPK","year":"2012"},{"key":"10.1016\/j.neunet.2022.09.014_b14","series-title":"Deep learning","author":"Goodfellow","year":"2016"},{"key":"10.1016\/j.neunet.2022.09.014_b15","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/3422622","article-title":"Generative adversarial networks","volume":"63","author":"Goodfellow","year":"2020","journal-title":"Communications of the ACM"},{"key":"10.1016\/j.neunet.2022.09.014_b16","series-title":"Gurobi optimizer reference manual","author":"Gurobi Optimization, LLC","year":"2021"},{"key":"10.1016\/j.neunet.2022.09.014_b17","first-page":"770","article-title":"Deep residual learning for image recognition","volume":"Vol. 2016-Decem","author":"He","year":"2016"},{"key":"10.1016\/j.neunet.2022.09.014_b18","first-page":"2261","article-title":"Densely connected convolutional networks","volume":"Vol. 2017-Janua","author":"Huang","year":"2017"},{"key":"10.1016\/j.neunet.2022.09.014_b19","doi-asserted-by":"crossref","unstructured":"Jared L, Adair, Kristin L, Detry, Richard J, Durfee, Justin D, Jones,\u00a0K., & A, Martin,\u00a0N. (2012). Comparison of Open-Source Linear Programming Solvers. United States: http:\/\/dx.doi.org\/10.2172\/1104761.","DOI":"10.2172\/1104761"},{"key":"10.1016\/j.neunet.2022.09.014_b20","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1038\/s41586-021-03819-2","article-title":"Highly accurate protein structure prediction with AlphaFold","volume":"596","author":"Jumper","year":"2021","journal-title":"Nature"},{"key":"10.1016\/j.neunet.2022.09.014_b21","doi-asserted-by":"crossref","unstructured":"Karmarkar,\u00a0N. (1984). A new polynomial-time algorithm for linear programming. In Proceedings of the sixteenth annual ACM symposium on theory of computing (pp. 302\u2013311).","DOI":"10.1145\/800057.808695"},{"key":"10.1016\/j.neunet.2022.09.014_b22","doi-asserted-by":"crossref","first-page":"5455","DOI":"10.1007\/s10462-020-09825-6","article-title":"A survey of the recent architectures of deep convolutional neural networks","volume":"53","author":"Khan","year":"2020","journal-title":"Artificial Intelligence Review"},{"key":"10.1016\/j.neunet.2022.09.014_b23","series-title":"Adam: A method for stochastic optimization","author":"Kingma","year":"2014"},{"key":"10.1016\/j.neunet.2022.09.014_b24","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1145\/3065386","article-title":"ImageNet classification with deep convolutional neural networks","volume":"60","author":"Krizhevsky","year":"2017","journal-title":"Communications of the ACM"},{"key":"10.1016\/j.neunet.2022.09.014_b25","series-title":"The handbook of brain theory and neural networks, 3361","first-page":"255","article-title":"Convolutional networks for images, speech, and time series","author":"LeCun","year":"1995"},{"key":"10.1016\/j.neunet.2022.09.014_b26","series-title":"Benchmarks of optimization software","author":"Mittelmann","year":"2022"},{"key":"10.1016\/j.neunet.2022.09.014_b27","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1073\/pnas.36.1.48","article-title":"Equilibrium points in n-person games","volume":"36","author":"Nash","year":"1950","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"10.1016\/j.neunet.2022.09.014_b28","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF01448847","article-title":"Zur Theorie der Gesellschaftsspiele","volume":"100","author":"von Neumann","year":"1928","journal-title":"Mathematische Annalen"},{"key":"10.1016\/j.neunet.2022.09.014_b29","article-title":"PyTorch: An imperative style, high-performance deep learning library","volume":"Vol. 32","author":"Paszke","year":"2019"},{"key":"10.1016\/j.neunet.2022.09.014_b30","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1038\/nature16961","article-title":"Mastering the game of Go with deep neural networks and tree search","volume":"529","author":"Silver","year":"2016","journal-title":"Nature"},{"key":"10.1016\/j.neunet.2022.09.014_b31","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1108\/md.1998.36.6.419.1","article-title":"Investment science","volume":"36","author":"Simmons","year":"1998","journal-title":"Management decision"},{"key":"10.1016\/j.neunet.2022.09.014_b32","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/67.795133","article-title":"Introduction to game theory and its application in electric power markets","volume":"12","author":"Singh","year":"1999","journal-title":"IEEE Computer Applications in Power"},{"key":"10.1016\/j.neunet.2022.09.014_b33","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/j.ejor.2019.01.010","article-title":"A second-order cone programming formulation for two player zero-sum games with chance constraints","volume":"275","author":"Singh","year":"2019","journal-title":"European Journal of Operational Research"},{"key":"10.1016\/j.neunet.2022.09.014_b34","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.jcp.2018.08.029","article-title":"DGM: A deep learning algorithm for solving partial differential equations","volume":"375","author":"Sirignano","year":"2018","journal-title":"Journal of Computational Physics"},{"key":"10.1016\/j.neunet.2022.09.014_b35","series-title":"EfficientNet: Rethinking model scaling for convolutional neural networks","author":"Tan","year":"2019"},{"key":"10.1016\/j.neunet.2022.09.014_b36","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1109\/TCYB.2018.2886238","article-title":"Deep learning meets game theory: Bregman-based algorithms for interactive deep generative adversarial networks","volume":"50","author":"Tembine","year":"2020","journal-title":"IEEE Transactions on Cybernetics"},{"key":"10.1016\/j.neunet.2022.09.014_b37","series-title":"Linear programming","first-page":"345","article-title":"Integer programming","author":"Vanderbei","year":"2014"},{"key":"10.1016\/j.neunet.2022.09.014_b38","series-title":"Economics and the theory of games","first-page":"1","author":"Vega-Redondo","year":"2003"},{"key":"10.1016\/j.neunet.2022.09.014_b39","series-title":"Primal-dual interior-point methods","author":"Wright","year":"1997"},{"key":"10.1016\/j.neunet.2022.09.014_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.neunet.2022.04.006","article-title":"A dynamical neural network approach for solving stochastic two-player zero-sum games","author":"Wu","year":"2022","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2022.09.014_b41","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2022.117545","article-title":"Using CNN for solving two-player zero-sum games","author":"Wu","year":"2022","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.neunet.2022.09.014_b42","doi-asserted-by":"crossref","DOI":"10.1016\/j.neunet.2022.06.031","article-title":"Convergence of deep convolutional neural networks","author":"Xu","year":"2022","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2022.09.014_b43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3158369","article-title":"Deep learning based recommender system: A survey and new perspectives","volume":"52","author":"Zhang","year":"2019","journal-title":"ACM Computing Surveys"},{"key":"10.1016\/j.neunet.2022.09.014_b44","article-title":"A survey of game theoretic approach for adversarial machine learning","volume":"9","author":"Zhou","year":"2019","journal-title":"Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608022003586?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608022003586?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:15:53Z","timestamp":1778544953000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893608022003586"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12]]},"references-count":44,"alternative-id":["S0893608022003586"],"URL":"https:\/\/doi.org\/10.1016\/j.neunet.2022.09.014","relation":{},"ISSN":["0893-6080"],"issn-type":[{"value":"0893-6080","type":"print"}],"subject":[],"published":{"date-parts":[[2022,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"MG-CNN: A deep CNN to predict saddle points of matrix games","name":"articletitle","label":"Article Title"},{"value":"Neural Networks","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neunet.2022.09.014","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2022 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}