{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:24:03Z","timestamp":1740108243783,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,4,22]],"date-time":"2016-04-22T00:00:00Z","timestamp":1461283200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11271243"],"award-info":[{"award-number":["11271243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s00186-016-0539-z","type":"journal-article","created":{"date-parts":[[2016,4,22]],"date-time":"2016-04-22T10:00:48Z","timestamp":1461319248000},"page":"183-204","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Robust canonical duality theory for solving nonconvex programming problems under data uncertainty"],"prefix":"10.1007","volume":"84","author":[{"given":"Linsong","family":"Shen","sequence":"first","affiliation":[]},{"given":"Yanjun","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Xiaomei","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,4,22]]},"reference":[{"key":"539_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.orl.2008.09.010","volume":"37","author":"A Beck","year":"2009","unstructured":"Beck A, Ben-Tal A (2009) Duality in robust optimization: primal worst equals dual best. Oper Res Lett 37:1\u20136","journal-title":"Oper Res Lett"},{"key":"539_CR2","first-page":"127","volume":"17","author":"SC Fang","year":"2009","unstructured":"Fang SC, Gao DY, Sheu RL, Xing WX (2009) Global optimization for a class of fractional programming problems. J Glob Optim 17:127\u2013160","journal-title":"J Glob Optim"},{"key":"539_CR3","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1016\/S0362-546X(99)00129-7","volume":"42","author":"DY Gao","year":"2000","unstructured":"Gao DY (2000) Analytic solution and triality theory for nonconvex and nonsmooth variational problems with applications. Nonlinear Anal 42:1161\u20131193","journal-title":"Nonlinear Anal"},{"key":"539_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3176-7","volume-title":"Duality principles in nonconvex systems: theory, methods and applications","author":"DY Gao","year":"2000","unstructured":"Gao DY (2000) Duality principles in nonconvex systems: theory, methods and applications. Kluwer Academic Publishers, Dordrecht"},{"key":"539_CR5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1023\/A:1026537630859","volume":"17","author":"DY Gao","year":"2000","unstructured":"Gao DY (2000) Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. J Glob Optim 17:127\u2013160","journal-title":"J Glob Optim"},{"key":"539_CR6","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1080\/02331930310001611501","volume":"52","author":"DY Gao","year":"2003","unstructured":"Gao DY (2003) Perfect duality theory and complete solutions to a class of global optimization problems. Optimization 52:467\u2013493","journal-title":"Optimization"},{"key":"539_CR7","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1023\/B:JOGO.0000048034.94449.e3","volume":"29","author":"DY Gao","year":"2004","unstructured":"Gao DY (2004) Canonical duality theory and solutions to constrained nonconvex quadratic programming. J Glob Optim 29:377\u2013399","journal-title":"J Glob Optim"},{"issue":"2","key":"539_CR8","doi-asserted-by":"crossref","first-page":"293","DOI":"10.3934\/jimo.2007.3.293","volume":"3","author":"DY Gao","year":"2007","unstructured":"Gao DY (2007) Solutions and optimality criteria to box constrained nonconvex minimization problems. J Ind Manag Optim 3(2):293\u2013304","journal-title":"J Ind Manag Optim"},{"key":"539_CR9","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1016\/j.compchemeng.2009.06.009","volume":"33","author":"DY Gao","year":"2009","unstructured":"Gao DY (2009) Canonical duality theory: theory, method, and applications in global optimization. Comput Chem 33:1964\u20131972","journal-title":"Comput Chem"},{"issue":"3","key":"539_CR10","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s10898-009-9399-x","volume":"45","author":"DY Gao","year":"2009","unstructured":"Gao DY, Ruan N, Sherali H (2009) Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality. J Glob Optim 45(3):473\u2013497","journal-title":"J Glob Optim"},{"issue":"3","key":"539_CR11","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s00186-007-0204-7","volume":"67","author":"DY Gao","year":"2008","unstructured":"Gao DY, Ruan N (2008) Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem. Math Methods Oper Res 67(3):479\u2013496","journal-title":"Math Methods Oper Res"},{"issue":"3","key":"539_CR12","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1090\/qam\/1012271","volume":"47","author":"DY Gao","year":"1989","unstructured":"Gao DY, Strang G (1989) Geometric nonlinearity: potential energy, complementary energy, and the gap function. Quart Appl Math 47(3):487\u2013504","journal-title":"Quart Appl Math"},{"key":"539_CR13","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1137\/080736090","volume":"20","author":"V Jeyakumar","year":"2009","unstructured":"Jeyakumar V, Lee GM, Li GY (2009) Alternative theorems for quadratic inequality systems and global quadratic optimization. SIAM J Optim 20:983\u20131001","journal-title":"SIAM J Optim"},{"key":"539_CR14","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s11081-008-9076-9","volume":"10","author":"V Jeyakumar","year":"2009","unstructured":"Jeyakumar V, Huy NQ, Li G (2009) Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization. Optim Eng 10:409\u2013503","journal-title":"Optim Eng"},{"issue":"3","key":"539_CR15","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1016\/j.na.2011.04.006","volume":"75","author":"V Jeyakumar","year":"2012","unstructured":"Jeyakumar V, Li GY, Lee GM (2012) Robust duality for generalized convex programming problems under data uncertainty. Nonlinear Anal Theory Methods Appl 75(3):1362\u20131373","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"539_CR16","doi-asserted-by":"crossref","first-page":"3384","DOI":"10.1137\/100791841","volume":"20","author":"V Jeyakumar","year":"2010","unstructured":"Jeyakumar V, Li GY (2010) Strong duality in robust convex programming: complete characterizations. SIAM J Optim 20:3384\u20133407","journal-title":"SIAM J Optim"},{"issue":"3","key":"539_CR17","doi-asserted-by":"crossref","first-page":"597","DOI":"10.4134\/CKMS.2013.28.3.597","volume":"28","author":"MH Kim","year":"2013","unstructured":"Kim MH (2013) Duality theorem and vector saddle point theorem for robust multiobjective optimization problem. Commun Korean Math Soc 28(3):597\u2013602","journal-title":"Commun Korean Math Soc"},{"key":"539_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.peva.2014.02.003","volume":"75\u201376","author":"N Ruan","year":"2014","unstructured":"Ruan N, Gao DY (2014) Global optimal solutions to a general sensor network localization problem. Perform Eval 75\u201376:1\u201316","journal-title":"Perform Eval"},{"key":"539_CR19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10107-006-0090-4","volume":"112","author":"A Shapiro","year":"2008","unstructured":"Shapiro A (2008) Stochastic programming approach to optimization under uncertainty. Math Program Ser B 112:183\u2013220","journal-title":"Math Program Ser B"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0539-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-016-0539-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0539-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T10:33:33Z","timestamp":1558607613000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-016-0539-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,22]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["539"],"URL":"https:\/\/doi.org\/10.1007\/s00186-016-0539-z","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"type":"print","value":"1432-2994"},{"type":"electronic","value":"1432-5217"}],"subject":[],"published":{"date-parts":[[2016,4,22]]}}}