{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:00:13Z","timestamp":1740182413746,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004152","name":"Instituto Politico de Macau","doi-asserted-by":"publisher","award":["98900028"],"award-info":[{"award-number":["98900028"]}],"id":[{"id":"10.13039\/501100004152","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SN Oper. Res. Forum"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s43069-021-00082-z","type":"journal-article","created":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T13:02:48Z","timestamp":1637240568000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Scalarization of Multiobjective Robust Optimization Problems"],"prefix":"10.1007","volume":"2","author":[{"given":"S.","family":"Khoshkhabar-amiranloo","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,2]]},"reference":[{"key":"82_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-8044-1","volume-title":"Post-Optimal Analysis in Linear Semi-Infinite Optimization","author":"MA Goberna","year":"2014","unstructured":"Goberna MA, L\u00f3pez MA (2014) Post-Optimal Analysis in Linear Semi-Infinite Optimization. Springer Briefs in Optimization. Springer, New York"},{"key":"82_CR2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400831050","volume-title":"Robust Optimization","author":"A Ben-Tal","year":"2009","unstructured":"Ben-Tal A, Ghaoui El, Nemirovski A (2009) Robust Optimization. Princeton University Press, Princeton"},{"issue":"3","key":"82_CR3","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1137\/080734510","volume":"53","author":"D Bertsimas","year":"2011","unstructured":"Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3), 464\u2013501","journal-title":"SIAM Rev"},{"key":"82_CR4","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1006\/jmaa.1994.1176","volume":"183","author":"S Shi","year":"1994","unstructured":"Shi S, Zheng Q, Zhuang D (1994) Set-valued robust mappings and approximatable mappings. J Math Anal Appl 183:706\u2013726","journal-title":"J Math Anal Appl"},{"key":"82_CR5","doi-asserted-by":"publisher","first-page":"59","DOI":"10.7151\/dmdico.1059","volume":"25","author":"A Hoffmann","year":"2005","unstructured":"Hoffmann A, Geletu A (2005) On robustness of set-valued maps and marginal value functions. Discuss Math Differ Incl Control Optim 25:59\u2013108","journal-title":"Discuss Math Differ Incl Control Optim"},{"key":"82_CR6","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1080\/02331934.2013.769104","volume":"62","author":"K Klamroth","year":"2013","unstructured":"Klamroth K, K\u00f6bis E, Sch\u00f6bel A, Tammer C (2013) A unified approach for different concepts of robustness and stochastic programming via nonlinear scalarizing functionals. Optimization 62:649\u2013671","journal-title":"Optimization"},{"issue":"1","key":"82_CR7","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.ejor.2014.03.013","volume":"239","author":"M Ehrgott","year":"2014","unstructured":"Ehrgott M, Ide J, Sch\u00f6bel A (2014) Minmax robustness for multiobjective optimization problems. Eur J Oper Res 239(1), 17\u201331","journal-title":"Eur J Oper Res"},{"issue":"1","key":"82_CR8","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s00186-014-0471-z","volume":"80","author":"J Ide","year":"2014","unstructured":"Ide J, K\u00f6bis E (2014) Concepts of efficiency for uncertain multiobjective optimization problems based on set order relations. Math Meth Oper Res 80(1), 99\u2013127","journal-title":"Math Meth Oper Res"},{"key":"82_CR9","unstructured":"Kuroiwa D (1999) Some duality theorems of set-valued optimization with natural criteria. In: Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis. World Scientific, River Edge, NJ 221\u2013228"},{"key":"82_CR10","doi-asserted-by":"crossref","unstructured":"Ide J, K\u00f6bis E, Kuroiwa D, Sch\u00f6bel A, Tammer C (2014) The relationship between multiobjective robustness concepts and set-valued optimization. Fix Point Theory A 83","DOI":"10.1186\/1687-1812-2014-83"},{"key":"82_CR11","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s00291-015-0418-7","volume":"38","author":"J Ide","year":"2016","unstructured":"Ide J, Sch\u00f6bel A (2016) Robustness for uncertain multiobjective optimization: a survey and analysis of different concepts. OR Spectr 38:235\u2013271","journal-title":"OR Spectr"},{"issue":"1\u20132","key":"82_CR12","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10479-015-1813-9","volume":"251","author":"GP Crespi","year":"2017","unstructured":"Crespi GP, Kuroiwa D, Rocca M (2017) Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization. Ann Oper Res 251(1\u20132), 89\u2013104","journal-title":"Ann Oper Res"},{"issue":"1","key":"82_CR13","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1007\/s10957-017-1196-y","volume":"179","author":"HZ Wei","year":"2018","unstructured":"Wei HZ, Chen RC, Li SJ (2018) A unified characterization of multiobjective robustness via separation. J Optim Theory Appl 179(1), 86\u201310","journal-title":"J Optim Theory Appl"},{"issue":"3","key":"82_CR14","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1007\/s10957-018-1256-y","volume":"177","author":"HZ Wei","year":"2018","unstructured":"Wei HZ, Chen RC, Li SJ (2018) Characterizations for optimality conditions of general robust optimization problems. J Optim Theory Appl 177(3), 835\u2013856","journal-title":"J Optim Theory Appl"},{"issue":"2","key":"82_CR15","doi-asserted-by":"crossref","first-page":"705","DOI":"10.3934\/jimo.2018066","volume":"15","author":"H-Z Wei","year":"2019","unstructured":"Wei H-Z, Chen C-R (2019) Three concepts of robust efficiency for uncertain multiobjective optimization problems via set order relations. J Ind Manag Optim 15(2), 705\u2013721","journal-title":"J Ind Manag Optim"},{"issue":"7","key":"82_CR16","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1080\/02331934.2018.1426582","volume":"67","author":"Y Ogata","year":"2018","unstructured":"Ogata Y, Tanaka T, Saito Y, Lee GM, Lee JH (2018) An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets. Optimization 67(7), 1067\u20131075","journal-title":"Optimization"},{"key":"82_CR17","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s10013-018-0283-1","volume":"46","author":"N Dinh","year":"2018","unstructured":"Dinh N, Long DH (2018) Complete Characterizations of Robust Strong Duality for Robust Vector Optimization Problems. Vietnam J Math 46:293\u2013328","journal-title":"Vietnam J Math"},{"issue":"3","key":"82_CR18","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1007\/s10957-019-01505-y","volume":"181","author":"QH Ansari","year":"2019","unstructured":"Ansari QH, K\u00f6bis E, Sharma PK (2019) Characterizations of multiobjective robustness via oriented distance function and image space analysis. J Optim Theory Appl 181(3), 817\u2013839","journal-title":"J Optim Theory Appl"},{"key":"82_CR19","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1080\/02331934.2018.1493108","volume":"67","author":"QH Ansari","year":"2018","unstructured":"Ansari QH, K\u00f6bis E, Sharma PK (2018) Characterizations of set relations with respect to variable domination structures via oriented distance function. Optimization 67: 1389\u20131407","journal-title":"Optimization"},{"issue":"2","key":"82_CR20","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s10957-018-1437-8","volume":"181","author":"J Chen","year":"2019","unstructured":"Chen J, K\u00f6bis E, Yao J-C (2019) Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. J Optim Theory Appl 181(2), 411\u2013436","journal-title":"J Optim Theory Appl"},{"issue":"1","key":"82_CR21","first-page":"2","volume":"38","author":"C Chen","year":"2019","unstructured":"Chen C, Wei Y (2019) Robust multiobjective portfolio optimization: a set order relations approach. J Comb Optim 38(1), 2\u201349","journal-title":"J Comb Optim"},{"issue":"5","key":"82_CR22","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1080\/00036811.2017.1404582","volume":"98","author":"HZ Wei","year":"2017","unstructured":"Wei HZ, Chen CR, Li SJ (2017) Robustness to uncertain optimization using scalarization techniques and relations to multiobjective optimization, Appl Anal 98(5), 851\u2013866","journal-title":"Appl Anal"},{"key":"82_CR23","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1007\/s10957-019-01609-5","volume":"184","author":"HZ Wei","year":"2020","unstructured":"Wei HZ, Chen CR, Li SJ (2020) A unified approach through image space analysis to robustness in uncertain optimization problems. J Optim Theory Appl 184:466\u2013493","journal-title":"J Optim Theory Appl"},{"key":"82_CR24","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10957-020-01709-7","volume":"186","author":"HZ Wei","year":"2020","unstructured":"Wei HZ, Chen CR, Li SJ (2020) Robustness characterizations for uncertain optimization problems via image space analysis. J Optim Theory Appl 186:459\u2013479","journal-title":"J Optim Theory Appl"},{"key":"82_CR25","doi-asserted-by":"publisher","first-page":"2750","DOI":"10.1080\/00036811.2015.1109079","volume":"95","author":"S Khoshkhabar-amiranloo","year":"2015","unstructured":"Khoshkhabar-amiranloo S, Khorram E (2015) Scalar characterizations of cone-continuous set-valued maps. Appl Anal 95:2750\u20132765","journal-title":"Appl Anal"},{"key":"82_CR26","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s11590-016-1027-3","volume":"11","author":"S Khoshkhabar-amiranloo","year":"2016","unstructured":"Khoshkhabar-amiranloo S, Khorram E, Soleimani-damaneh M (2016) Nonlinear scalarization functions and polar cone in set optimization. Optim Lett 11:521\u2013535","journal-title":"Optim Lett"},{"key":"82_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jmaa.2006.01.033","volume":"325","author":"H Hern\u00e1ndez","year":"2007","unstructured":"Hern\u00e1ndez H, Rodr\u00edguez-Mar\u00edn L (2007) Nonconvex scalarization in set optimization with set-valued maps. J Math Anal Appl 325:1\u201318","journal-title":"J Math Anal Appl"},{"key":"82_CR28","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1007\/s10957-013-0363-z","volume":"167","author":"J Jahn","year":"2013","unstructured":"Jahn J (2013) Vectorization in set optimization. J Optim Theory Appl 167:783\u2013795","journal-title":"J Optim Theory Appl"}],"container-title":["Operations Research Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-021-00082-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s43069-021-00082-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-021-00082-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,15]],"date-time":"2023-01-15T19:39:20Z","timestamp":1673811560000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s43069-021-00082-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,2]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["82"],"URL":"https:\/\/doi.org\/10.1007\/s43069-021-00082-z","relation":{},"ISSN":["2662-2556"],"issn-type":[{"type":"electronic","value":"2662-2556"}],"subject":[],"published":{"date-parts":[[2021,8,2]]},"assertion":[{"value":"7 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No potential conflict of interest was reported by the author.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure Statement"}}],"article-number":"40"}}