{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:46:54Z","timestamp":1770756414390,"version":"3.50.0"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"SERB, India","award":["MTR\/2021\/000696"],"award-info":[{"award-number":["MTR\/2021\/000696"]}]},{"name":"SERB, India","award":["CRG\/2022\/001347"],"award-info":[{"award-number":["CRG\/2022\/001347"]}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12071379"],"award-info":[{"award-number":["12071379"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100005230","name":"Natural Science Foundation of Chongqing","doi-asserted-by":"crossref","award":["cstc2021jcyj-msxmX0925, cstc2022ycjh-bgzxm0097"],"award-info":[{"award-number":["cstc2021jcyj-msxmX0925, cstc2022ycjh-bgzxm0097"]}],"id":[{"id":"10.13039\/501100005230","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Youth Project of Science and Technology Research Program of Chongqing Education Commission of China","award":["KJQN202201802"],"award-info":[{"award-number":["KJQN202201802"]}]},{"name":"MOST, Taiwan","award":["11-2115-M-039-001-MY2"],"award-info":[{"award-number":["11-2115-M-039-001-MY2"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s40314-025-03151-9","type":"journal-article","created":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T02:58:18Z","timestamp":1742698698000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Epsilon-subdifferentiability for interval-valued functions and its application in interval optimization problems"],"prefix":"10.1007","volume":"44","author":[{"given":"Krishan","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2419-7082","authenticated-orcid":false,"given":"Debdas","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiawei","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jen-Chih","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"issue":"3","key":"3151_CR1","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1504\/IJMOR.2017.087208","volume":"11","author":"I Ahmad","year":"2017","unstructured":"Ahmad I, Singh D, Dar BA (2017) Optimality and duality in non-differentiable interval valued multiobjective programming. International Journal of Mathematics in Operational Research 11(3):332\u2013356","journal-title":"International Journal of Mathematics in Operational Research"},{"issue":"1","key":"3151_CR2","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1007\/s10957-018-1431-1","volume":"181","author":"DTV An","year":"2019","unstructured":"An DTV, Yao JC (2019) Differential stability of convex optimization problems with possibly empty solution sets. Journal of Optimization Theory and Applications 181(1):126\u2013143","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"4","key":"3151_CR3","first-page":"1","volume":"41","author":"D Anshika Ghosh","year":"2022","unstructured":"Anshika Ghosh D (2022) Interval-valued value function and its application in interval optimization problems. Computational and Applied Mathematics 41(4):1\u201326","journal-title":"Computational and Applied Mathematics"},{"issue":"4","key":"3151_CR4","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1016\/S0252-9602(17)30062-0","volume":"37","author":"T Antczak","year":"2017","unstructured":"Antczak T (2017) Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function. Acta Mathematica Scientia 37(4):1133\u20131150","journal-title":"Acta Mathematica Scientia"},{"issue":"3","key":"3151_CR5","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s11228-016-0388-1","volume":"26","author":"C Audet","year":"2018","unstructured":"Audet C, Hare W (2018) Algorithmic construction of the subdifferential from directional derivatives. Set-Valued and Variational Analysis 26(3):431\u2013447","journal-title":"Set-Valued and Variational Analysis"},{"key":"3151_CR6","volume-title":"Convex Analysis and Optimization","author":"C Bandle","year":"1982","unstructured":"Bandle C, Aubin JP, Vinter RB (1982) Convex Analysis and Optimization, vol 57. Addison-Wesley Longman Limited"},{"key":"3151_CR7","volume-title":"Convex Optimization Algorithms","author":"D Bertsekas","year":"2015","unstructured":"Bertsekas D (2015) Convex Optimization Algorithms. Athena Scientific, Belmont"},{"issue":"1","key":"3151_CR8","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s00500-018-3100-6","volume":"23","author":"SK Bharati","year":"2019","unstructured":"Bharati SK, Singh S (2019) Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment. Soft Computing 23(1):77\u201384","journal-title":"Soft Computing"},{"issue":"2","key":"3151_CR9","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1137\/0805022","volume":"5","author":"JR Birge","year":"1995","unstructured":"Birge JR, Qi L (1995) Subdifferential convergence in stochastic programs. SIAM Journal on Optimization 5(2):436\u2013453","journal-title":"SIAM Journal on Optimization"},{"key":"3151_CR10","doi-asserted-by":"crossref","unstructured":"Br\u00f8ndsted A, Rockafellar RT (1965) On the subdifferentiability of convex functions. Proceedings of the American Mathematical Society 16(4):605\u2013611","DOI":"10.1090\/S0002-9939-1965-0178103-8"},{"issue":"11","key":"3151_CR11","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1016\/j.ins.2011.01.023","volume":"181","author":"Y Chalco-Cano","year":"2011","unstructured":"Chalco-Cano Y, Roman-Flores H, Jim\u00e9nez-Gamero MD (2011) Generalized derivative and $$\\pi $$-derivative for set-valued functions. Information Sciences 181(11):2177\u20132188","journal-title":"Information Sciences"},{"issue":"3","key":"3151_CR12","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s10700-013-9156-y","volume":"12","author":"Y Chalco-Cano","year":"2013","unstructured":"Chalco-Cano Y, Lodwick WA, Rufi\u00e1n-Lizana A (2013) Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optimization and Decision Making 12(3):305\u2013322","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"3151_CR13","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.fss.2019.04.006","volume":"375","author":"Y Chalco-Cano","year":"2019","unstructured":"Chalco-Cano Y, Maqui-Huam\u00e1n GG, Silva GN, Jim\u00e9nez-Gamero MD (2019) Algebra of generalized Hukuhara differentiable interval-valued functions: review and new properties. Fuzzy Sets and Systems 375:53\u201369","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"3151_CR14","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1016\/0377-2217(95)00055-0","volume":"94","author":"S Chanas","year":"1996","unstructured":"Chanas S, Kuchta D (1996) Multiobjective programming in optimization of interval objective functions-a generalized approach. European Journal of Operational Research 94(3):594\u2013598","journal-title":"European Journal of Operational Research"},{"key":"3151_CR15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.ins.2020.12.034","volume":"559","author":"RS Chauhan","year":"2021","unstructured":"Chauhan RS, Ghosh D (2021) An erratum to extended karush-kuhn-tucker condition for constrained interval optimization problems and its application in support vector machines. Information Sciences 559:309\u2013313","journal-title":"Information Sciences"},{"issue":"23","key":"3151_CR16","doi-asserted-by":"crossref","first-page":"14629","DOI":"10.1007\/s00500-021-06251-w","volume":"25","author":"RS Chauhan","year":"2021","unstructured":"Chauhan RS, Ghosh D, Ramik J, Debnath AK (2021) Generalized Hukuhara-Clarke derivative of interval-valued functions and its properties. Soft Computing 25(23):14629\u201314643","journal-title":"Soft Computing"},{"issue":"11","key":"3151_CR17","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1016\/j.finel.2003.09.006","volume":"40","author":"SH Chen","year":"2004","unstructured":"Chen SH, Wu J, Chen YD (2004) Interval optimization for uncertain structures. Finite Elements in Analysis and Design 40(11):1379\u20131398","journal-title":"Finite Elements in Analysis and Design"},{"issue":"2","key":"3151_CR18","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1137\/18M1169370","volume":"29","author":"R Correa","year":"2019","unstructured":"Correa R, Hantoute A, L\u00f3pez-Cerd\u00e1 MA (2019) Moreau-Rockafellar-type formulas for the subdifferential of the supremum function. SIAM Journal on Optimization 29(2):1106\u20131130","journal-title":"SIAM Journal on Optimization"},{"issue":"1\u20132","key":"3151_CR19","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1007\/s12190-016-0990-2","volume":"53","author":"D Ghosh","year":"2017","unstructured":"Ghosh D (2017) Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions. Journal of Applied Mathematics and Computing 53(1\u20132):709\u2013731","journal-title":"Journal of Applied Mathematics and Computing"},{"key":"3151_CR20","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.ins.2019.07.017","volume":"504","author":"D Ghosh","year":"2019","unstructured":"Ghosh D, Singh A, Shukla K, Manchanda K (2019) Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines. Information Sciences 504:276\u2013292","journal-title":"Information Sciences"},{"key":"3151_CR21","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.ijar.2020.03.004","volume":"121","author":"D Ghosh","year":"2020","unstructured":"Ghosh D, Debnath AK, Pedrycz W (2020) A variable and a fixed ordering of intervals and their application in optimization with interval-valued functions. International Journal of Approximate Reasoning 121:187\u2013205","journal-title":"International Journal of Approximate Reasoning"},{"key":"3151_CR22","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.ins.2019.09.023","volume":"510","author":"D Ghosh","year":"2020","unstructured":"Ghosh D, Chauhan RS, Mesiar R, Debnath AK (2020) Generalized Hukuhara G\u00e2teaux and Fr\u00e9chet derivatives of interval-valued functions and their application in optimization with interval-valued functions. Information Sciences 510:317\u2013340","journal-title":"Information Sciences"},{"issue":"2","key":"3151_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12046-022-01815-4","volume":"47","author":"D Ghosh","year":"2022","unstructured":"Ghosh D, Debnath AK, Chauhan RS, Mesiar R (2022) Generalized-Hukuhara subgradient and its application in optimization problem with interval-valued functions. S\u0101dhan\u0101 47(2):1\u201316","journal-title":"S\u0101dhan\u0101"},{"issue":"2","key":"3151_CR24","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF02191853","volume":"82","author":"BM Glover","year":"1994","unstructured":"Glover BM, Craven BD (1994) A Fritz John optimality condition using the approximate subdifferential. Journal of Optimization Theory and Applications 82(2):253\u2013265","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"2","key":"3151_CR25","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s10444-015-9426-z","volume":"42","author":"P Grohs","year":"2016","unstructured":"Grohs P, Hosseini S (2016) $$\\varepsilon $$-subgradient algorithms for locally Lipschitz functions on Riemannian manifolds. Advances in Computational Mathematics 42(2):333\u2013360","journal-title":"Advances in Computational Mathematics"},{"issue":"1","key":"3151_CR26","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.jmaa.2005.02.017","volume":"310","author":"C Guti\u00e9rrez","year":"2005","unstructured":"Guti\u00e9rrez C, Jim\u00e9nez B, Novo V (2005) A chain rule for $$\\epsilon $$-subdifferentials with applications to approximate solutions in convex Pareto problems. Journal of Mathematical Analysis and Applications 310(1):309\u2013327","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"3151_CR27","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.na.2012.11.016","volume":"79","author":"C Guti\u00e9rrez","year":"2013","unstructured":"Guti\u00e9rrez C, Huerga L, Jim\u00e9nez B, Novo V (2013) Proper approximate solutions and $$\\varepsilon $$-subdifferentials in vector optimization: basic properties and limit behaviour. Nonlinear Analysis: Theory, Methods & Applications 79:52\u201367","journal-title":"Nonlinear Analysis: Theory, Methods & Applications"},{"issue":"2","key":"3151_CR28","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1137\/070700413","volume":"19","author":"A Hantoute","year":"2008","unstructured":"Hantoute A, L\u00f3pez MA, Z\u0103linescu C (2008) Subdifferential calculus rules in convex analysis: a unifying approach via pointwise supremum functions. SIAM Journal on Optimization 19(2):863\u2013882","journal-title":"SIAM Journal on Optimization"},{"key":"3151_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-06409-2","volume-title":"Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods","author":"JB Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty JB, Lemar\u00e9chal C (1993) Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods. Springer-Verlag, Berlin Heidelberg"},{"key":"3151_CR30","unstructured":"Hiriart-Urruty J, Phelps R (1982) $$\\varepsilon $$-subdifferential calculus. In Convex Analysis and Optimization, Pitman, New York pp. 43\u201392"},{"issue":"3","key":"3151_CR31","first-page":"205","volume":"10","author":"M Hukuhara","year":"1967","unstructured":"Hukuhara M (1967) Int\u00e9gration des applications mesurables dont la valeur est un compact convexe. Funkcialaj Ekvacioj 10(3):205\u2013223","journal-title":"Funkcialaj Ekvacioj"},{"issue":"5","key":"3151_CR32","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/S0893-9659(03)00071-5","volume":"16","author":"M Ida","year":"2003","unstructured":"Ida M (2003) Portfolio selection problem with interval coefficients. Applied Mathematics Letters 16(5):709\u2013713","journal-title":"Applied Mathematics Letters"},{"issue":"3","key":"3151_CR33","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/0377-2217(94)00092-Q","volume":"86","author":"M Inuiguchi","year":"1995","unstructured":"Inuiguchi M, Sakawa M (1995) Minimax regret solution to linear programming problems with an interval objective function. European Journal of Operational Research 86(3):526\u2013536","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"3151_CR34","first-page":"389","volume":"281","author":"A Ioffe","year":"1984","unstructured":"Ioffe A (1984) Approximate subdifferentials and applications. I: The finite-dimensional theory. Transactions of the American Mathematical Society 281(1):389\u2013416","journal-title":"Transactions of the American Mathematical Society"},{"issue":"2","key":"3151_CR35","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0377-2217(90)90375-L","volume":"48","author":"H Ishibuchi","year":"1990","unstructured":"Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research 48(2):219\u2013225","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"3151_CR36","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s12351-013-0137-2","volume":"14","author":"M Jana","year":"2014","unstructured":"Jana M, Panda G (2014) Solution of nonlinear interval vector optimization problem. Operational Research 14(1):71\u201385","journal-title":"Operational Research"},{"key":"3151_CR37","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF00138691","volume":"8","author":"V Jeyakumar","year":"1996","unstructured":"Jeyakumar V, Glover BM (1996) Characterizing global optimality for DC optimization problems under convex inequality constraints. Journal of Global Optimization 8:171\u2013187","journal-title":"Journal of Global Optimization"},{"issue":"1","key":"3151_CR38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2007.03.031","volume":"188","author":"C Jiang","year":"2008","unstructured":"Jiang C, Han X, Liu G, Liu G (2008) A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research 188(1):1\u201313","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"3151_CR39","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/s40314-022-02173-x","volume":"42","author":"G Kumar","year":"2023","unstructured":"Kumar G, Ghosh D (2023) Ekeland\u2019s variational principle for interval-valued functions. Computational and Applied Mathematics 42(1):28","journal-title":"Computational and Applied Mathematics"},{"issue":"19","key":"3151_CR40","doi-asserted-by":"crossref","first-page":"10253","DOI":"10.1007\/s00500-022-07332-0","volume":"26","author":"K Kumar","year":"2022","unstructured":"Kumar K, Ghosh D, Kumar G (2022) Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability. Soft Computing 26(19):10253\u201310273","journal-title":"Soft Computing"},{"key":"3151_CR41","doi-asserted-by":"crossref","unstructured":"Li L (2022) Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders. Fuzzy Optimization and Decision Making pp. 1\u201319","DOI":"10.1007\/s10700-022-09391-2"},{"key":"3151_CR42","doi-asserted-by":"crossref","unstructured":"M\u00e4kel\u00e4 MM, Neittaanm\u00e4ki P (1992) Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control. World Scientific","DOI":"10.1142\/1493"},{"issue":"18","key":"3151_CR43","doi-asserted-by":"crossref","first-page":"9427","DOI":"10.1016\/j.amc.2012.03.027","volume":"218","author":"MT Malinowski","year":"2012","unstructured":"Malinowski MT (2012) Second type Hukuhara differentiable solutions to the delay set-valued differential equations. Applied Mathematics and Computation 218(18):9427\u20139437","journal-title":"Applied Mathematics and Computation"},{"key":"3151_CR44","volume-title":"Interval Analysis","author":"RE Moore","year":"1966","unstructured":"Moore RE (1966) Interval Analysis, vol 4. Prentice-Hall Englewood Cliffs, NJ"},{"key":"3151_CR45","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1023\/A:1018985914065","volume":"81","author":"F Mr\u00e1z","year":"1998","unstructured":"Mr\u00e1z F (1998) Calculating the exact bounds of optimal values in LP with interval coefficients. Annals of Operations Research 81:51\u201362","journal-title":"Annals of Operations Research"},{"issue":"1","key":"3151_CR46","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s101079900112","volume":"87","author":"P Neame","year":"2000","unstructured":"Neame P, Boland N, Ralph D (2000) An outer approximate subdifferential method for piecewise affine optimization. Mathematical Programming 87(1):57\u201386","journal-title":"Mathematical Programming"},{"issue":"3\u20134","key":"3151_CR47","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1016\/j.na.2008.12.005","volume":"71","author":"L Stefanini","year":"2009","unstructured":"Stefanini L, Bede B (2009) Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis: Theory, Methods & Applications 71(3\u20134):1311\u20131328","journal-title":"Nonlinear Analysis: Theory, Methods & Applications"},{"issue":"3","key":"3151_CR48","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0165-0114(94)90097-3","volume":"66","author":"SC Tong","year":"1994","unstructured":"Tong SC (1994) Interval number and fuzzy number linear programmings. Fuzzy Sets and Systems 66(3):301\u2013306","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"3151_CR49","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s10288-017-0369-8","volume":"16","author":"D Van Luu","year":"2018","unstructured":"Van Luu D, Mai TT (2018) Optimality and duality in constrained interval-valued optimization. 4OR 16(3):311\u2013337","journal-title":"4OR"},{"issue":"2","key":"3151_CR50","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/BF01100690","volume":"5","author":"M Volle","year":"1994","unstructured":"Volle M (1994) Calculus rules for global approximate minima and applications to approximate subdifferential calculus. Journal of Global Optimization 5(2):131\u2013157","journal-title":"Journal of Global Optimization"},{"issue":"1","key":"3151_CR51","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.ejor.2005.09.007","volume":"176","author":"HC Wu","year":"2007","unstructured":"Wu HC (2007) The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function. European Journal of Operational Research 176(1):46\u201359","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"3151_CR52","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.jmaa.2007.05.023","volume":"338","author":"HC Wu","year":"2008","unstructured":"Wu HC (2008) On interval-valued nonlinear programming problems. Journal of Mathematical Analysis and Applications 338(1):299\u2013316","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"3","key":"3151_CR53","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s10957-008-9396-0","volume":"138","author":"HC Wu","year":"2008","unstructured":"Wu HC (2008) Wolfe duality for interval-valued optimization. Journal of Optimization Theory and Applications 138(3):497\u2013509","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"3151_CR54","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.ejor.2008.03.012","volume":"196","author":"HC Wu","year":"2009","unstructured":"Wu HC (2009) The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions. European Journal of Operational Research 196(1):49\u201360","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"3151_CR55","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s10957-009-9613-5","volume":"144","author":"H Wu","year":"2010","unstructured":"Wu H (2010) Duality theory for optimization problems with interval-valued objective functions. Journal of Optimization Theory and Applications 144(3):615\u2013628","journal-title":"Journal of Optimization Theory and Applications"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03151-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03151-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03151-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:27:01Z","timestamp":1744604821000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03151-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,22]]},"references-count":55,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["3151"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03151-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,22]]},"assertion":[{"value":"8 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"197"}}