{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:46:22Z","timestamp":1740123982152,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,2,9]],"date-time":"2019-02-09T00:00:00Z","timestamp":1549670400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100008736","name":"Fondo de Fomento al Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1181316"],"award-info":[{"award-number":["1181316"]}],"id":[{"id":"10.13039\/501100008736","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s10957-019-01486-y","type":"journal-article","created":{"date-parts":[[2019,2,9]],"date-time":"2019-02-09T12:27:20Z","timestamp":1549715240000},"page":"787-816","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems"],"prefix":"10.1007","volume":"181","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2485-7861","authenticated-orcid":false,"given":"Fabi\u00e1n","family":"Flores-Baz\u00e1n","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giandomenico","family":"Mastroeni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristi\u00e1n","family":"Vera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,2,9]]},"reference":[{"key":"1486_CR1","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1137\/120861400","volume":"23","author":"F Flores-Baz\u00e1n","year":"2013","unstructured":"Flores-Baz\u00e1n, F., Mastroeni, G.: Strong duality in cone constrained nonconvex optimization. SIAM J. Optim. 23, 153\u2013169 (2013)","journal-title":"SIAM J. Optim."},{"key":"1486_CR2","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1007\/s10898-017-0542-9","volume":"69","author":"F Flores-Baz\u00e1n","year":"2017","unstructured":"Flores-Baz\u00e1n, F., Echegaray, W., Flores-Baz\u00e1n, F., Oca\u00f1a, E.: Primal or dual strong duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap. J. Glob. Optim. 69, 823\u2013845 (2017)","journal-title":"J. Glob. Optim."},{"key":"1486_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-28020-0","volume-title":"Constrained Optimization and Image Space Analysis","author":"F Giannessi","year":"2005","unstructured":"Giannessi, F.: Constrained Optimization and Image Space Analysis. Springer, New York (2005)"},{"key":"1486_CR4","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/BF00935321","volume":"60","author":"F Giannessi","year":"1984","unstructured":"Giannessi, F.: Theorems of the alternative and optimality conditions. J. Optim. Theory Appl. 60, 331\u2013365 (1984)","journal-title":"J. Optim. Theory Appl."},{"doi-asserted-by":"crossref","unstructured":"Fullerton, R.E., Braunschweiger, C.C.: Quasi-interior points of cones. Technical Report No. 2, University of Delaware, Department of Mathematics (1963)","key":"1486_CR5","DOI":"10.21236\/AD0423950"},{"issue":"1992","key":"1486_CR6","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF01581072","volume":"57","author":"JM Borwein","year":"1992","unstructured":"Borwein, J.M., Lewis, A.S.: Partially finite convex programming, part I: quasi relative interiors and duality theory. Math. Program. Ser. A 57(1992), 15\u201348 (1992)","journal-title":"Math. Program. Ser. A"},{"key":"1486_CR7","doi-asserted-by":"publisher","first-page":"2542","DOI":"10.1023\/A:1022988116044","volume":"115","author":"JM Borwein","year":"2003","unstructured":"Borwein, J.M., Goebel, R.: Notions of relative interior in Banach spaces. J. Math. Sci. 115, 2542\u20132553 (2003)","journal-title":"J. Math. Sci."},{"key":"1486_CR8","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s10957-004-1724-4","volume":"125","author":"F Cammaroto","year":"2005","unstructured":"Cammaroto, F., Di Bella, B.: Separation theorem based on the quasirelative interior in convex optimization. J. Optim. Theory Appl. 125, 223\u2013229 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR9","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1137\/07068432X","volume":"19","author":"RI Bot","year":"2008","unstructured":"Bot, R.I., Csetnek, E.R., Wanka, G.: Regularity conditions via quasi-relative interior in convex programming. SIAM J. Optim. 19, 217\u2013233 (2008)","journal-title":"SIAM J. Optim."},{"key":"1486_CR10","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/978-3-642-21114-0_2","volume-title":"Recent Developments in Vector Optimization","author":"F Flores-Baz\u00e1n","year":"2012","unstructured":"Flores-Baz\u00e1n, F., Flores-Baz\u00e1n, F., Vera, C.: Gordan-type alternative theorems and vector optimization revisited. In: Ansari, Q.H., Yao, J.C. (eds.) Recent Developments in Vector Optimization, pp. 29\u201359. Springer, Berlin (2012)"},{"key":"1486_CR11","doi-asserted-by":"publisher","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces","author":"C Z\u0103linescu","year":"2002","unstructured":"Z\u0103linescu, C.: Convex Analysis in General Vector Spaces. World Scientific Publishing Co., Inc., River Edge (2002)"},{"key":"1486_CR12","doi-asserted-by":"publisher","first-page":"1795","DOI":"10.1080\/02331934.2015.1032284","volume":"64","author":"C Z\u01celinescu","year":"2015","unstructured":"Z\u01celinescu, C.: On the use of quasi-relative interior in optimization. Optimization 64, 1795\u20131823 (2015)","journal-title":"Optimization"},{"key":"1486_CR13","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10957-011-9844-0","volume":"150","author":"ZA Zhou","year":"2011","unstructured":"Zhou, Z.A., Yang, X.M.: Optimality conditions of generalized subconvexlike set-valued optimization problems based on the quasi-relative interior. J. Optim. Theory Appl. 150, 327\u2013340 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR14","first-page":"1007","volume":"21","author":"B Hern\u00e1ndez-Jim\u00e9nez","year":"2014","unstructured":"Hern\u00e1ndez-Jim\u00e9nez, B., Osuna-Gomez, R., Rojas-Medar, M.A.: Characterization of weakly efficient solutions for nonlinear multiobjective programming problems. Duality. J. Convex Anal. 21, 1007\u20131022 (2014)","journal-title":"J. Convex Anal."},{"key":"1486_CR15","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s11590-006-0028-z","volume":"1","author":"P Daniele","year":"2007","unstructured":"Daniele, P., Giuffr\u00e8, S.: General infinite dimensional duality and applications to evolutionary networks equilibrium problems. Optim. Lett. 1, 227\u2013243 (2007)","journal-title":"Optim. Lett."},{"key":"1486_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02886-1","volume-title":"Duality in Vector Optimization","author":"RI Bot","year":"2009","unstructured":"Bot, R.I., Grad, S.M., Wanka, G.: Duality in Vector Optimization. Springer, Berlin (2009)"},{"key":"1486_CR17","first-page":"85","volume-title":"Optimization in Economics, Finance and Industry (Verona)","author":"G Bigi","year":"2002","unstructured":"Bigi, G.: Saddlepoint optimality criteria in vector optimization. In: Guerraggio, A., et al. (eds.) Optimization in Economics, Finance and Industry (Verona), pp. 85\u2013102. Datanova, Milan (2002)"},{"key":"1486_CR18","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1016\/j.jmaa.2011.12.050","volume":"389","author":"C Guti\u00e9rrez","year":"2012","unstructured":"Guti\u00e9rrez, C., Huerga, L., Novo, V.: Scalarization and saddle points of approximate proper solutions in nearly subconvexlike vector optimization problems. J. Math. Anal. Appl. 389, 1046\u20131058 (2012)","journal-title":"J. Math. Anal. Appl."},{"key":"1486_CR19","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/978-3-642-21114-0_6","volume-title":"Recent Developments in Vector Optimization","author":"G Mastroeni","year":"2012","unstructured":"Mastroeni, G.: Optimality conditions and image space analysis for vector optimization problems. In: Ansari, Q.H., Yao, J.-C. (eds.) Recent Developments in Vector Optimization, pp. 169\u2013220. Springer, Berlin (2012)"},{"key":"1486_CR20","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s10957-008-9412-4","volume":"139","author":"RI Bot","year":"2008","unstructured":"Bot, R.I., Csetnek, E.R., Moldovan, A.: Revisiting some duality theorems via the quasirelative interior in convex optimization. J. Optim. Theory Appl. 139, 67\u201384 (2008)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR21","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.jmaa.2009.09.006","volume":"361","author":"A Grad","year":"2010","unstructured":"Grad, A.: Quasi-relative interior-type constraint qualifications ensuring strong Lagrange duality for optimization problems with cone and affine constraints. J. Math. Anal. Appl. 361, 86\u201395 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"1486_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24828-6","volume-title":"Vector Optimization\u2014Theory, Applications and extensions","author":"J Jahn","year":"2004","unstructured":"Jahn, J.: Vector Optimization\u2014Theory, Applications and extensions. Springer, Berlin (2004)"},{"key":"1486_CR23","series-title":"Lecture Notes in Economics and Mathematical Systems","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-50280-4","volume-title":"Theory of Vector Optimization","author":"DT Luc","year":"1989","unstructured":"Luc, D.T.: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, New York (1989)"},{"key":"1486_CR24","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1137\/0315004","volume":"15","author":"J Borwein","year":"1977","unstructured":"Borwein, J.: Proper efficient points for maximizations with respect to cones. SIAM J. Control Optim. 15, 57\u201363 (1977)","journal-title":"SIAM J. Control Optim."},{"key":"1486_CR25","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/BF00940705","volume":"78","author":"MA Limber","year":"1993","unstructured":"Limber, M.A., Goodrich, R.K.: Quasi interiors, Lagrange multipliers, and $$L^p$$ L p spectral estimation with lattice bounds. J. Optim. Theory Appl. 78, 143\u2013161 (1993)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR26","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1007\/s10898-013-0073-y","volume":"58","author":"SM Guu","year":"2014","unstructured":"Guu, S.M., Li, J.: Vector quasi-equilibrium problems: separation, saddle points and error bounds for the solution set. J. Glob. Optim. 58, 751\u2013767 (2014)","journal-title":"J. Glob. Optim."},{"key":"1486_CR27","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.jmaa.2004.10.001","volume":"307","author":"X-H Gong","year":"2005","unstructured":"Gong, X.-H.: Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior. J. Math. Anal. Appl. 307, 12\u201331 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"1486_CR28","first-page":"109","volume":"4","author":"WW Brecker","year":"1997","unstructured":"Brecker, W.W., Kassay, G.: A systematization of convexity concepts for sets and functions. J. Convex Anal. 4, 109\u2013127 (1997)","journal-title":"J. Convex Anal."},{"key":"1486_CR29","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1007\/BF01580450","volume":"8","author":"R Lehmann","year":"1975","unstructured":"Lehmann, R., Oettli, W.: The theorem of the alternative, the key-theorem, and the vector-maximum problem. Math. Program. 8, 332\u2013344 (1975)","journal-title":"Math. Program."},{"key":"1486_CR30","doi-asserted-by":"publisher","first-page":"915","DOI":"10.1007\/s11590-017-1164-3","volume":"12","author":"SM Grad","year":"2018","unstructured":"Grad, S.M.: Characterizations via linear scalarization of minimal and properly minimal elements. Optim. Lett. 12, 915\u2013922 (2018)","journal-title":"Optim. Lett."},{"key":"1486_CR31","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059130","volume-title":"Ordered Linear Spaces","author":"GJO Jameson","year":"1970","unstructured":"Jameson, G.J.O.: Ordered Linear Spaces. Lecture Notes in Mathematics, vol. 141. Springer, Heidelberg (1970)"},{"key":"1486_CR32","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1090\/S0002-9939-1955-0068113-7","volume":"6","author":"VL Klee","year":"1955","unstructured":"Klee, V.L.: Separation properties of convex cones. Proc. Am. Math. Soc. 6, 313\u2013318 (1955)","journal-title":"Proc. Am. Math. Soc."},{"key":"1486_CR33","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s10107-008-0249-2","volume":"122","author":"TQ Bao","year":"2010","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Relative Pareto minimizers for multiobjective problems: existence and optimality conditions. Math. Program. Ser. A 122, 301\u2013347 (2010)","journal-title":"Math. Program. Ser. A"},{"key":"1486_CR34","doi-asserted-by":"publisher","first-page":"1399","DOI":"10.1080\/02331934.2011.641018","volume":"60","author":"F Flores-Baz\u00e1n","year":"2011","unstructured":"Flores-Baz\u00e1n, F., Hern\u00e1ndez, E.: A unified vector optimization problem: complete scalarizations and applications. Optimization 60, 1399\u20131419 (2011)","journal-title":"Optimization"},{"key":"1486_CR35","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s10898-011-9822-y","volume":"56","author":"F Flores-Baz\u00e1n","year":"2013","unstructured":"Flores-Baz\u00e1n, F., Hern\u00e1ndez, E.: Optimality conditions for a unified vector optimization problem with not necessarily preordering relations. J. Glob. Optim. 56, 299\u2013315 (2013)","journal-title":"J. Glob. Optim."},{"key":"1486_CR36","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10957-016-0880-7","volume":"69","author":"J Li","year":"2016","unstructured":"Li, J., Mastroeni, G.: Image convexity of generalized systems with infinite-dimensional image and applications. J. Optim. Theory Appl. 69, 91\u2013115 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR37","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/0022-247X(79)90226-9","volume":"71","author":"HP Benson","year":"1979","unstructured":"Benson, H.P.: An improved definition of proper efficiency for vector maximization with respect to cones. J. Math. Anal. Appl. 71, 232\u2013241 (1979)","journal-title":"J. Math. Anal. Appl."},{"key":"1486_CR38","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s10957-006-9140-6","volume":"131","author":"R Zeng","year":"2006","unstructured":"Zeng, R., Caron, R.J.: Generalized Motzkin Gordan alternative theorems and vector optimization problems. J. Optim. Theory Appl. 131, 281\u2013289 (2006)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR39","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/BF00938802","volume":"60","author":"F Tardella","year":"1989","unstructured":"Tardella, F.: On the image of a constrained extremum problem and some applications to the existence of a minimum. J. Optim. Theory Appl. 60, 93\u2013104 (1989)","journal-title":"J. Optim. Theory Appl."},{"key":"1486_CR40","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"1486_CR41","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1090\/S0002-9904-1941-07494-X","volume":"47","author":"LL Dines","year":"1941","unstructured":"Dines, L.L.: On the mapping of quadratic forms. Bull. Am. Math. Soc. 47, 494\u2013498 (1941)","journal-title":"Bull. Am. Math. Soc."},{"key":"1486_CR42","first-page":"257","volume":"1","author":"F Flores-Baz\u00e1n","year":"2016","unstructured":"Flores-Baz\u00e1n, F., Opazo, F.: Characterizing the convexity of joint-range for a pair of inhomogeneous quadratic functions and strong duality. Minimax Theory Appl. 1, 257\u2013290 (2016)","journal-title":"Minimax Theory Appl."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-019-01486-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01486-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01486-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T14:18:43Z","timestamp":1694614723000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-019-01486-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,9]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["1486"],"URL":"https:\/\/doi.org\/10.1007\/s10957-019-01486-y","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2019,2,9]]},"assertion":[{"value":"24 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 February 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}