{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:54:06Z","timestamp":1772297646750,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,5,19]],"date-time":"2011-05-19T00:00:00Z","timestamp":1305763200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2011,10]]},"DOI":"10.1007\/s10957-011-9859-6","type":"journal-article","created":{"date-parts":[[2011,5,18]],"date-time":"2011-05-18T13:31:12Z","timestamp":1305725472000},"page":"135-162","source":"Crossref","is-referenced-by-count":23,"title":["Stochastic Multiobjective Optimization: Sample Average Approximation and Applications"],"prefix":"10.1007","volume":"151","author":[{"given":"J\u00f6rg","family":"Fliege","sequence":"first","affiliation":[]},{"given":"Huifu","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,5,19]]},"reference":[{"key":"9859_CR1","volume-title":"Multiobjective Decision Analysis with Engineering and Business Applications","author":"A. Goicoechea","year":"1982","unstructured":"Goicoechea, A., Hansen, D.R., Duckstein, L.: Multiobjective Decision Analysis with Engineering and Business Applications. Wiley, New York (1982)"},{"key":"9859_CR2","volume-title":"Stochastic Programming with Multi-Objective Functions","author":"I.M. Stancu-Minasian","year":"1984","unstructured":"Stancu-Minasian, I.M.: Stochastic Programming with Multi-Objective Functions. Reidel, Dordrecht (1984)"},{"key":"9859_CR3","volume-title":"Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty","year":"1990","unstructured":"Slowinski, R., Teghem, J. (eds.): Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty. Kluwer Academic, Dordrecht (1990)"},{"key":"9859_CR4","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1023\/A:1017591412366","volume":"110","author":"R. Caballero","year":"2001","unstructured":"Caballero, R., Cerda, E., Munoz, M.M., Rey, L.: Efficient solution concepts and their relations in stochastic multiobjective programming. J. Optim. Theory Appl. 110, 53\u201374 (2001)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"9859_CR5","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10107-002-0365-3","volume":"96","author":"J.J. Ye","year":"2003","unstructured":"Ye, J.J., Zhu, Q.J.: Multiobjective optimization problems with variational inequality constraints. Math. Program. 96(1), 139\u2013160 (2003)","journal-title":"Math. Program."},{"key":"9859_CR6","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10107-007-0172-y","volume":"117","author":"B.S. Mordukhovich","year":"2009","unstructured":"Mordukhovich, B.S.: Multiobjective optimization problems with equilibrium constraints. Math. Program. 117, 331\u2013354 (2009)","journal-title":"Math. Program."},{"key":"9859_CR7","volume-title":"Optimality and Efficiency","author":"D.J. White","year":"1982","unstructured":"White, D.J.: Optimality and Efficiency. Wiley, Chichester (1982)"},{"key":"9859_CR8","first-page":"618","volume":"22","author":"A.M. Geoffrion","year":"1968","unstructured":"Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. J. Optim. Theory Appl. 22, 618\u2013630 (1968)","journal-title":"J. Optim. Theory Appl."},{"key":"9859_CR9","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s001860300316","volume":"59","author":"J. Fliege","year":"2004","unstructured":"Fliege, J.: Gap-free computation of Pareto-points by quadratic scalarizations. Math. Methods Oper. Res. 59, 69\u201389 (2004)","journal-title":"Math. Methods Oper. Res."},{"issue":"4","key":"9859_CR10","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1287\/moor.1060.0221","volume":"31","author":"J. Fliege","year":"2006","unstructured":"Fliege, J.: An efficient interior-point method for convex multicriteria optimization problems. Math. Oper. Res. 31(4), 825\u2013845 (2006)","journal-title":"Math. Oper. Res."},{"key":"9859_CR11","unstructured":"Ben Abdelaziz, F.: L\u2018efficacit\u00e9 en programmation multi-objectifs stochastique. Ph.D. Thesis, Universit\u00e9 de Laval, Quebec (1992)"},{"key":"9859_CR12","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/S0377-2217(03)00371-0","volume":"158","author":"R. Caballero","year":"2004","unstructured":"Caballero, R., Cerda, E., Munoz, M.M., Rey, L.: Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems. Eur. J. Oper. Res. 158, 633\u2013648 (2004)","journal-title":"Eur. J. Oper. Res."},{"key":"9859_CR13","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1080\/17442509108833676","volume":"34","author":"A.J. King","year":"1991","unstructured":"King, A.J., Wets, R.J.-B.: Epi-consistency of convex stochastic programs. Stoch. Stoch. Rep. 34, 83\u201392 (1991)","journal-title":"Stoch. Stoch. Rep."},{"key":"9859_CR14","first-page":"137","volume":"75","author":"E.L. Plambeck","year":"1996","unstructured":"Plambeck, E.L., Fu, B.R., Robinson, S.M., Suri, R.: Sample-path optimization of convex stochastic performances functions. Math. Program. 75, 137\u2013176 (1996)","journal-title":"Math. Program."},{"key":"9859_CR15","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1287\/moor.21.3.513","volume":"21","author":"S.M. Robinson","year":"1996","unstructured":"Robinson, S.M.: Analysis of sample-path optimization. Math. Oper. Res. 21, 513\u2013528 (1996)","journal-title":"Math. Oper. Res."},{"key":"9859_CR16","series-title":"Handbooks in OR & MS","volume-title":"Stochastic Programming","author":"A. Shapiro","year":"2003","unstructured":"Shapiro, A.: Monte Carlo sampling methods. In: Rusczy\u0144ski, A., Shapiro, A. (eds.) Stochastic Programming. Handbooks in OR & MS, vol.\u00a010. North-Holland, Amsterdam (2003)"},{"key":"9859_CR17","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1287\/moor.1070.0260","volume":"32","author":"H. Xu","year":"2007","unstructured":"Xu, H., Meng, F.: Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints. Math. Oper. Res. 32, 648\u2013668 (2007)","journal-title":"Math. Oper. Res."},{"key":"9859_CR18","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1287\/opre.1080.0686","volume":"57","author":"V. Miguel De","year":"2009","unstructured":"De Miguel, V., Xu, H.: A stochastic multiple leader Stackelberg model: analysis, computation, and application. Oper. Res. 57, 1220\u20131235 (2009)","journal-title":"Oper. Res."},{"key":"9859_CR19","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.orl.2008.05.003","volume":"36","author":"W. Wang","year":"2008","unstructured":"Wang, W., Ahmed, S.: Sample average approximation of expected value constrained stochastic programs. Oper. Res. Lett. 36, 515\u2013519 (2008)","journal-title":"Oper. Res. Lett."},{"key":"9859_CR20","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/978-1-4757-6388-1_15","volume-title":"Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods","author":"J. Peng","year":"1998","unstructured":"Peng, J.: A smoothing function and its applications. In: Fukushima, M., Qi, L. (eds.) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, pp.\u00a0293\u2013316. Kluwer Academic, Dordrecht (1998)"},{"key":"9859_CR21","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/B978-044450263-6\/50015-4","volume-title":"Handbook of Measure Theory","author":"C. Hess","year":"2002","unstructured":"Hess, C.: Set-valued integration and set-valued probability theory: an overview. In: Handbook of Measure Theory, vols.\u00a0I, II, pp.\u00a0617\u2013673. North-Holland, Amsterdam (2002)"},{"key":"9859_CR22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10957-006-9136-2","volume":"131","author":"J. Fliege","year":"2006","unstructured":"Fliege, J., Vicente, L.N.: A\u00a0multicriteria approach to bilevel optimization. J. Optim. Theory Appl. 131, 209\u2013225 (2006)","journal-title":"J. Optim. Theory Appl."},{"key":"9859_CR23","volume-title":"Mathematics of Decision Theory. Methods and Models in the Social Sciences","author":"P.C. Fishburn","year":"1972","unstructured":"Fishburn, P.C.: Mathematics of Decision Theory. Methods and Models in the Social Sciences. Mouton, The Hague (1972)"},{"key":"9859_CR24","series-title":"Systems in Economics","volume-title":"Vektoroptimierung in Produktr\u00e4umen","author":"W. Vogel","year":"1977","unstructured":"Vogel, W.: Vektoroptimierung in Produktr\u00e4umen. Systems in Economics, vol.\u00a035. Hain, Meisenheim am Glan (1977)"},{"key":"9859_CR25","series-title":"Mathematics in Science and Engineering","volume-title":"Theory of Multiobjective Optimization","author":"Y. Sawaragi","year":"1985","unstructured":"Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Mathematics in Science and Engineering, vol.\u00a0176. Academic Press, San Diego (1985)"},{"key":"9859_CR26","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/BF00939390","volume":"58","author":"R. Durier","year":"1988","unstructured":"Durier, R.: Weighting factor results in vector optimization. J. Optim. Theory Appl. 58, 411\u2013430 (1988)","journal-title":"J. Optim. Theory Appl."},{"key":"9859_CR27","first-page":"481","volume-title":"Contributions to the Theory of Games","author":"K.J. Arrow","year":"1953","unstructured":"Arrow, K.J., Barankin, E.W., Blackwell, D.: Admissible points of convex sets. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, pp.\u00a0481\u2013492. Princeton University Press, Princeton (1953)"},{"key":"9859_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-24828-6","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":"9859_CR29","series-title":"Mathematisch-Naturwissenschaftliche Bibliothek","volume-title":"Vektoroptimierung\u2014Theorie, Verfahren und Anwendungen","author":"A. G\u00f6pfert","year":"1990","unstructured":"G\u00f6pfert, A., Nehse, R.: Vektoroptimierung\u2014Theorie, Verfahren und Anwendungen. Mathematisch-Naturwissenschaftliche Bibliothek, vol.\u00a074. Teubner, Leipzig (1990)"},{"key":"9859_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)"},{"key":"9859_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems. Springer Series in Operations Research","author":"J.F. Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer Series in Operations Research. Springer, New York (2000)"},{"key":"9859_CR32","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF00932614","volume":"14","author":"P.L. Yu","year":"1974","unstructured":"Yu, P.L.: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiple objectives. J. Optim. Theory Appl. 14, 319\u2013377 (1974)","journal-title":"J. Optim. Theory Appl."},{"key":"9859_CR33","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/02331930801954177","volume":"57","author":"A. Shapiro","year":"2008","unstructured":"Shapiro, A., Xu, H.: Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation. Optimization 57, 395\u2013418 (2008)","journal-title":"Optimization"},{"key":"9859_CR34","volume-title":"Set-Valued Analysis","author":"J.-P. Aubin","year":"1990","unstructured":"Aubin, J.-P., Frankowska, H.: Set-Valued Analysis. Birkh\u00e4user, Boston (1990)"},{"key":"9859_CR35","first-page":"79","volume-title":"Nonsmooth Optimization","author":"C. Lemar\u00e9chal","year":"1978","unstructured":"Lemar\u00e9chal, C.: Bundle methods in nonsmooth optimization. In: Lemar\u00e9chal, C., Mifflin, R. (eds.) Nonsmooth Optimization, pp.\u00a079\u2013102. Pergamon Press, Oxford (1978)"},{"key":"9859_CR36","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1287\/moor.12.1.32","volume":"12","author":"A. Rusczy\u0144ski","year":"1987","unstructured":"Rusczy\u0144ski, A.: A linearization method for nonsmooth stochastic programming problems. Math. Oper. Res. 12, 32\u201349 (1987)","journal-title":"Math. Oper. Res."},{"key":"9859_CR37","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1023\/A:1004649211111","volume":"106","author":"L. Dai","year":"2000","unstructured":"Dai, L., Chen, C.H., Birge, J.R.: Convergence properties of two stage stochastic programming. J.\u00a0Optim. Theory Appl. 106, 489\u2013509 (2000)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9859_CR38","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF02204815","volume":"30","author":"A. Shapiro","year":"1991","unstructured":"Shapiro, A.: Asymptotic analysis of stochastic programs. Ann. Oper. Res. 30, 169\u2013186 (1991)","journal-title":"Ann. Oper. Res."},{"key":"9859_CR39","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF01582215","volume":"67","author":"A. Shapiro","year":"1994","unstructured":"Shapiro, A.: Quantitative stability in stochastic programming. Math. Program. 67, 99\u2013108 (1994)","journal-title":"Math. Program."},{"key":"9859_CR40","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1137\/0806028","volume":"6","author":"W. R\u00f6misch","year":"1996","unstructured":"R\u00f6misch, W., Schultz, R.: Lipschitz stability for stochastic programs with complete recourse. SIAM J. Optim. 6, 531\u2013547 (1996)","journal-title":"SIAM J. Optim."},{"key":"9859_CR41","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/S1052623496307510","volume":"8","author":"I. Das","year":"1998","unstructured":"Das, I., Dennis, J.E.: Normal-boundary intersection: a new method for generating Pareto optimal points in nonlinear multicriteria optimization problems. SIAM J. Optim. 8, 631\u2013657 (1998)","journal-title":"SIAM J. Optim."},{"key":"9859_CR42","volume-title":"Proceedings of the 7th AIAA\/USAF Conference","author":"Y. Li","year":"1998","unstructured":"Li, Y., Fadel, G.M., Wiecek, M.M.: Approximating Pareto curves using the hyper-ellipse. In: Proceedings of the 7th AIAA\/USAF Conference (1998)"},{"key":"9859_CR43","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s10479-006-0058-z","volume":"147","author":"T.K. Ralphs","year":"2006","unstructured":"Ralphs, T.K., Saltzman, M.J., Wiecek, M.M.: An improved algorithm for solving bi-objective integer programs. Ann. Oper. Res. 147, 43\u201370 (2006)","journal-title":"Ann. Oper. Res."},{"key":"9859_CR44","unstructured":"Xu, H., Zhang, D.: Stochastic Nash equilibrium problems: sample average approximation and applications. Available at http:\/\/www.optimization-online.org (2009)"},{"key":"9859_CR45","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8280-4","volume-title":"Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach","author":"C. Hillermeier","year":"2001","unstructured":"Hillermeier, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkh\u00e4user, Basel (2001)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-011-9859-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-011-9859-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-011-9859-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T18:15:35Z","timestamp":1560190535000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-011-9859-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,19]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["9859"],"URL":"https:\/\/doi.org\/10.1007\/s10957-011-9859-6","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5,19]]}}}