{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T20:56:57Z","timestamp":1775077017353,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T00:00:00Z","timestamp":1522627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100007224","name":"National Foundation for Science and Technology Development","doi-asserted-by":"publisher","award":["101.04-2016.05"],"award-info":[{"award-number":["101.04-2016.05"]}],"id":[{"id":"10.13039\/100007224","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2016R1A2B4011589"],"award-info":[{"award-number":["NRF-2016R1A2B4011589"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s10107-018-1271-7","type":"journal-article","created":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T07:44:22Z","timestamp":1522655062000},"page":"321-341","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["On the existence of Pareto solutions for polynomial vector optimization problems"],"prefix":"10.1007","volume":"177","author":[{"given":"Do Sang","family":"Kim","sequence":"first","affiliation":[]},{"given":"Ti\u1ebfn-S\u01a1n","family":"Ph\u1ea1m","sequence":"additional","affiliation":[]},{"given":"Nguyen Van","family":"Tuyen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,4,2]]},"reference":[{"key":"1271_CR1","doi-asserted-by":"publisher","first-page":"1542","DOI":"10.1137\/140980624","volume":"25","author":"T Bajbar","year":"2015","unstructured":"Bajbar, T., Stein, O.: Coercive polynomials and their Newton polytopes. SIAM J. Optim. 25, 1542\u20131570 (2015)","journal-title":"SIAM J. Optim."},{"key":"1271_CR2","first-page":"531","volume":"36","author":"TQ Bao","year":"2007","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Variational principles for set-valued mappings with applications to multiobjective optimization. Control Cybern. 36, 531\u2013562 (2007)","journal-title":"Control Cybern."},{"key":"1271_CR3","doi-asserted-by":"publisher","first-page":"101","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. 122, 101\u2013138 (2010)","journal-title":"Math. Program."},{"key":"1271_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03718-8","volume-title":"Real Algebraic Geometry","author":"J Bochnak","year":"1998","unstructured":"Bochnak, J., Coste, M., Roy, M.-F.: Real Algebraic Geometry. Springer, Berlin (1998)"},{"key":"1271_CR5","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1287\/moor.8.1.64","volume":"8","author":"JM Borwein","year":"1983","unstructured":"Borwein, J.M.: On the existence of Pareto efficient points. Math. Oper. Res. 8, 64\u201373 (1983)","journal-title":"Math. Oper. Res."},{"key":"1271_CR6","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1112\/jtopol\/jts005","volume":"5","author":"LRG Dias","year":"2012","unstructured":"Dias, L.R.G., Ruas, M.A.S., Tib\u0103r, M.: Regularity at infinity of real mappings and a Morse\u2013Sard theorem. J. Topol. 5, 323\u2013340 (2012)","journal-title":"J. Topol."},{"key":"1271_CR7","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s00209-014-1369-4","volume":"279","author":"LRG Dias","year":"2015","unstructured":"Dias, L.R.G., Tib\u0103r, M.: Detecting bifurcation values at infinity of real polynomials. Math. Z. 279, 311\u2013319 (2015)","journal-title":"Math. Z."},{"key":"1271_CR8","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1007\/s10208-016-9303-2","volume":"17","author":"LRG Dias","year":"2017","unstructured":"Dias, L.R.G., Tanab\u00e9, S., Tib\u0103r, M.: Toward effective detection of the bifurcation locus of real polynomial maps. Found. Comput. Math. 17, 837\u2013849 (2017)","journal-title":"Found. Comput. Math."},{"key":"1271_CR9","unstructured":"\u0110inh, S.T., H\u00e0, H.V., Ph\u1ea1m, T.S.: A Frank\u2013Wolfe type theorem and H\u00f6lder-type global error bound for generic polynomial systems. Preprint 2012, VIASM. Available online from \n                              http:\/\/viasm.edu.vn\/wp-content\/uploads\/2012\/11\/Preprint_1227.pdf"},{"key":"1271_CR10","unstructured":"\u0110inh, S.T., H\u00e0, H.V., Ph\u1ea1m, T.S.: A Frank\u2013Wolfe type theorem for nondegenerate polynomial programs. Math. Program. Ser. A. 147, 519\u2013538 (2014)"},{"key":"1271_CR11","volume-title":"Multicriteria Optimization","author":"M Ehrgott","year":"2005","unstructured":"Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2005)"},{"key":"1271_CR12","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/S0022-4049(02)00121-4","volume":"179","author":"JF Fernando","year":"2003","unstructured":"Fernando, J.F., Gamboa, J.M.: Polynomial images of \n                              $${\\mathbb{R}}^{n}$$\n                              \n                                 \n                                 \n                                    \n                                       \n                                          R\n                                       \n                                       n\n                                    \n                                 \n                              \n                              \n                           . J. Pure Appl. Algebra 179, 241\u2013254 (2003)","journal-title":"J. Pure Appl. Algebra"},{"key":"1271_CR13","unstructured":"Fernando, J.F., Gamboa, J.M., Ueno, C.: The open quadrant problem: a topological proof. In: A Mathematical Tribute to Professor Jos\u00e9 Mar\u00eda Montesinos Amilibia, pp. 337\u2013350. Dep. Geom. Topol. Fac. Cien. Mat. UCM, Madrid (2016)"},{"key":"1271_CR14","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.jsc.2016.08.004","volume":"79","author":"JF Fernando","year":"2017","unstructured":"Fernando, J.F., Ueno, C.: A short proof for the open quadrant problem. J. Symb. Comput. 79, 57\u201364 (2017)","journal-title":"J. Symb. Comput."},{"key":"1271_CR15","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/s10957-014-0541-7","volume":"162","author":"C Guti\u00e9rrez","year":"2014","unstructured":"Guti\u00e9rrez, C., L\u00f3pez, R., Novo, V.: Existence and boundedness of solutions in infinite-dimensional vector optimization problems. J. Optim. Theory Appl. 162, 515\u2013547 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"1271_CR16","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/j.jmaa.2005.04.044","volume":"316","author":"TXD H\u00e0","year":"2006","unstructured":"H\u00e0, T.X.D.: Variants of the Ekeland variational principle for a set-valued map involving the Clarke normal cone. J. Math. Anal. Appl. 316, 346\u2013356 (2006)","journal-title":"J. Math. Anal. Appl."},{"key":"1271_CR17","unstructured":"H\u00e0, T.X.D.: Private communication (2017)"},{"key":"1271_CR18","first-page":"141","volume":"32","author":"HV H\u00e0","year":"2007","unstructured":"H\u00e0, H.V., Ph\u1ea1m, T.S.: An estimation of the number of bifurcation values for real polynomials. Acta Math. Vietnam. 32, 141\u2013153 (2007)","journal-title":"Acta Math. Vietnam."},{"key":"1271_CR19","doi-asserted-by":"publisher","DOI":"10.1142\/q0066","volume-title":"Genericity in Polynomial Optimization","author":"HV H\u00e0","year":"2017","unstructured":"H\u00e0, H.V., Ph\u1ea1m, T.S.: Genericity in Polynomial Optimization. World Scientific Publishing, Singapore (2017)"},{"key":"1271_CR20","doi-asserted-by":"publisher","first-page":"1060","DOI":"10.1137\/15M1041134","volume":"26","author":"NTT Huong","year":"2016","unstructured":"Huong, N.T.T., Yao, J.-C., Yen, N.D.: Polynomial vector variational inequalities under polynomial constraints and applications. SIAM J. Optim. 26, 1060\u20131071 (2016)","journal-title":"SIAM J. Optim."},{"key":"1271_CR21","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1016\/j.jmaa.2007.01.104","volume":"335","author":"A Ioffe","year":"2007","unstructured":"Ioffe, A.: A Sard theorem for tame set-valued mappings. J. Math. Anal. Appl. 335, 882\u2013901 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"1271_CR22","volume-title":"Vector Optimization. Theory Applications, and Extensions","author":"J Jahn","year":"2004","unstructured":"Jahn, J.: Vector Optimization. Theory Applications, and Extensions. Springer, Berlin (2004)"},{"key":"1271_CR23","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s002090100298","volume":"239","author":"Z Jelonek","year":"2002","unstructured":"Jelonek, Z.: Geometry of real polynomial mappings. Math. Z. 239, 321\u2013333 (2002)","journal-title":"Math. Z."},{"key":"1271_CR24","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s00209-013-1213-2","volume":"276","author":"Z Jelonek","year":"2014","unstructured":"Jelonek, Z., Kurdyka, K.: Reaching generalized critical values of a polynomial. Math. Z. 276, 557\u2013570 (2014)","journal-title":"Math. Z."},{"key":"1271_CR25","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1007\/s10957-014-0545-3","volume":"163","author":"V Jeyakumar","year":"2014","unstructured":"Jeyakumar, V., Lasserre, J.B., Li, G.: On polynomial optimization over non-compact semi-algebraic sets. J. Optim. Theory Appl. 163, 707\u2013718 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"1271_CR26","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/BF01077143","volume":"11","author":"AG Khovanskii","year":"1978","unstructured":"Khovanskii, A.G.: Newton polyhedra and toroidal varieties. Funct. Anal. Appl. 11, 289\u2013296 (1978)","journal-title":"Funct. Anal. Appl."},{"key":"1271_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01389769","volume":"32","author":"AG Kouchnirenko","year":"1976","unstructured":"Kouchnirenko, A.G.: Polyhedres de Newton et nombre de Milnor. Invent. Math. 32, 1\u201331 (1976)","journal-title":"Invent. Math."},{"key":"1271_CR28","doi-asserted-by":"publisher","first-page":"67","DOI":"10.4310\/jdg\/1090347525","volume":"56","author":"K Kurdyka","year":"2000","unstructured":"Kurdyka, K., Orro, P., Simon, S.: Semialgebraic Sard theorem for generalized critical values. J. Differ. Geom. 56, 67\u201392 (2000)","journal-title":"J. Differ. Geom."},{"key":"1271_CR29","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1215\/ijm\/1256044935","volume":"42","author":"TL Loi","year":"1998","unstructured":"Loi, T.L., Zaharia, A.: Bifurcation sets of functions definable in o-minimal structures. Ill. J. Math. 42, 449\u2013457 (1998)","journal-title":"Ill. J. Math."},{"key":"1271_CR30","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1016\/j.orl.2014.07.007","volume":"42","author":"V Magron","year":"2014","unstructured":"Magron, V., Henrion, D., Lasserre, J.B.: Approximating Pareto curves using semidefinite relaxations. Oper. Res. Lett. 42, 432\u2013437 (2014)","journal-title":"Oper. Res. Lett."},{"key":"1271_CR31","doi-asserted-by":"publisher","first-page":"2143","DOI":"10.1137\/140992047","volume":"25","author":"V Magron","year":"2015","unstructured":"Magron, V., Henrion, D., Lasserre, J.B.: Semidefinite approximations of projections and polynomial images of semialgebraic sets. SIAM J. Optim. 25, 2143\u20132164 (2015)","journal-title":"SIAM J. Optim."},{"key":"1271_CR32","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/s11784-010-0019-7","volume":"7","author":"J Mawhin","year":"2010","unstructured":"Mawhin, J., Willem, M.: Origin and evolution of the Palais\u2013Smale condition in critical point theory. J. Fixed Point Theory Appl. 7, 265\u2013290 (2010)","journal-title":"J. Fixed Point Theory Appl."},{"key":"1271_CR33","unstructured":"Motzkin, T.: The arithmetic-geometric inequalities. In: Shisha O. (ed.) Inequalities. Proceeding Symposium on Wright-Patterson Air Force Base, OH, 19\u201327 Aug 1965, pp. 205\u2013224. Academic Press (1967)"},{"key":"1271_CR34","doi-asserted-by":"publisher","first-page":"681","DOI":"10.2977\/prims\/1195170853","volume":"26","author":"A N\u00e9methi","year":"1990","unstructured":"N\u00e9methi, A., Zaharia, A.: On the bifurcation set of a polynomial function and Newton boundary. Publ. Res. Inst. Math. Sci. 26, 681\u2013689 (1990)","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"1271_CR35","doi-asserted-by":"publisher","first-page":"269","DOI":"10.2996\/kmj\/1138043796","volume":"20","author":"L P\u0103unescu","year":"1997","unstructured":"P\u0103unescu, L., Zaharia, A.: On the \u0141ojasiewicz exponent at infinity for polynomial functions. Kodai Math. J. 20, 269\u2013274 (1997)","journal-title":"Kodai Math. J."},{"key":"1271_CR36","doi-asserted-by":"publisher","first-page":"647","DOI":"10.2307\/2952457","volume":"146","author":"PJ Rabier","year":"1997","unstructured":"Rabier, P.J.: Ehresmann fibrations and Palais\u2013Smale conditions for morphisms of Finsler manifolds. Ann. Math. 146, 647\u2013691 (1997)","journal-title":"Ann. Math."},{"key":"1271_CR37","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1215\/S0012-7094-96-08416-1","volume":"84","author":"L Dries van den","year":"1996","unstructured":"van den Dries, L., Miller, C.: Geometric categories and o-minimal structures. Duke Math. J. 84, 497\u2013540 (1996)","journal-title":"Duke Math. J."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1271-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-018-1271-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1271-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T14:40:16Z","timestamp":1568904016000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-018-1271-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,2]]},"references-count":37,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["1271"],"URL":"https:\/\/doi.org\/10.1007\/s10107-018-1271-7","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,2]]},"assertion":[{"value":"8 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}