{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T12:52:28Z","timestamp":1770814348298,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Global Optimization"],"published-print":{"date-parts":[[2002,1]]},"DOI":"10.1023\/a:1013875600711","type":"journal-article","created":{"date-parts":[[2002,12,28]],"date-time":"2002-12-28T18:50:27Z","timestamp":1041101427000},"page":"285-317","source":"Crossref","is-referenced-by-count":77,"title":["Optimization over the efficient set: overview"],"prefix":"10.1007","volume":"22","author":[{"given":"Yoshitsugu","family":"Yamamoto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"383107_CR1","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"F.A. Al-Khayyal","year":"1983","unstructured":"Al-Khayyal, F.A. and Falk, J.E. (1983), Jointly constrained biconvex programming. Mathematics of Operations Research 8, 273\u2013286.","journal-title":"Mathematics of Operations Research"},{"key":"383107_CR2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0167-6377(96)00022-3","volume":"19","author":"L.T.H. An","year":"1996","unstructured":"An, L.T.H., Tao, P.D. and Muu, L.D. (1996), Numerical solution for optimization over the efficient set by d.c. optimization algorithms. Operations Research Letters 19, 117\u2013128.","journal-title":"Operations Research Letters"},{"key":"383107_CR3","first-page":"3","volume-title":"Optimization and Optimal Control","author":"M. Atteia","year":"1981","unstructured":"Atteia, M. and El Qortobi, Quasi-convex duality. In Optimization and Optimal Control,Lecture Notes in Control and Information Science 35, Springer, Berlin, 1981, pp. 3\u20138."},{"key":"383107_CR4","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BF00120667","volume":"1","author":"H.P. Benson","year":"1991","unstructured":"Benson, H.P. (1991), An all-linear programming relaxation algorithm for optimizing over the efficient set. Journal of Global Optimization 1, 83\u2013104.","journal-title":"Journal of Global Optimization"},{"key":"383107_CR5","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/BF00940077","volume":"73","author":"H.P. Benson","year":"1992","unstructured":"Benson, H.P. (1992), A finite nonadjacent extreme-point search algorithm for optimization over the efficient set. Journal of Optimization Theory and Applications 73, 47\u201364.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383107_CR6","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BF01099463","volume":"6","author":"H.P. Benson","year":"1995","unstructured":"Benson, H.P. (1995), A geometric analysis of the efficient outcome set in multiple objective convex program with linear criteria functions. Journal of Global Optimization 6, 213\u2013251.","journal-title":"Journal of Global Optimization"},{"key":"383107_CR7","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BF02192023","volume":"88","author":"H.P. Benson","year":"1996","unstructured":"Benson, H.P. and Lee, D. (1996), Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming. Journal of Optimization Theory and Applications 88, 77\u2013105.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383107_CR8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF02196590","volume":"80","author":"H.P. Benson","year":"1994","unstructured":"Benson, H.P. and Sayin, S. (1994), Optimization over the efficient set: four special case. Journal of Optimization Theory and Applications 80, 3\u201318.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383107_CR9","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF01582141","volume":"61","author":"S. Bolintineanu","year":"1993","unstructured":"Bolintineanu, S. (1993), Minimization of a quasi-concave function over an efficient set. Mathematical Programming 61, 89\u2013110.","journal-title":"Mathematical Programming"},{"key":"383107_CR10","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0167-6377(91)90042-N","volume":"10","author":"P.C. Chen","year":"1991","unstructured":"Chen, P.C., Hansen, P. and Jaumard, B. (1991), On-line and off-line vertex enumeration by adjacency lists. Operations Research Letters 10, 403\u2013409.","journal-title":"Operations Research Letters"},{"key":"383107_CR11","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF01279451","volume":"7","author":"J.P. Dauer","year":"1995","unstructured":"Dauer, J.P. and Fosnaugh, T.A. (1995), Optimization over the efficient set. Journal of Global Optimization 7, 261\u2013277.","journal-title":"Journal of Global Optimization"},{"key":"383107_CR12","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/BF02207641","volume":"83","author":"J.G. Ecker","year":"1994","unstructured":"Ecker, J.G. and Song, J.H. (1994), Optimizing a linear function over an efficient set. Journal of Optimization Theory and Applications 83, 541\u2013563.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383107_CR13","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/978-3-642-46802-5_28","volume-title":"Generalized Convexity","author":"J. F\u00fcl\u00f6p","year":"1994","unstructured":"F\u00fcl\u00f6p, J. (1994), A cutting plane algorithm for linear optimization over the efficient set. In S. Koml\u00f6si, T. Rapcs\u00e0k and S. Shaible (eds.), Generalized Convexity, Lecture Notes in Economics and Mathematical Systems 405, Springer, Berlin, pp. 374\u2013385."},{"key":"383107_CR14","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"M.R. Garay","year":"1979","unstructured":"Garay, M.R. and Johnson, D.S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco."},{"key":"383107_CR15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/0167-6377(88)90071-5","volume":"7","author":"R. Horst","year":"1988","unstructured":"Horst, R., de Vries, J. and Thoai, N.V. (1988), On finding new vertices and redundant constraints in cutting plane algorithms for global optimization. Operations Research Letters 7, 85\u201390.","journal-title":"Operations Research Letters"},{"key":"383107_CR16","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0377-2217(98)00230-6","volume":"117","author":"R. Horst","year":"1999","unstructured":"Horst, R. and Thoai, N.V. (1999), Maximizing a concave function over the efficient or weaklyefficient set. European Journal of Operational Research 117, 239\u2013252.","journal-title":"European Journal of Operational Research"},{"key":"383107_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03199-5","volume-title":"Global Optimization: Deterministic Approach","author":"R. Horst","year":"1996","unstructured":"Horst, R. and Tuy, H. (1996), Global Optimization: Deterministic Approach. Springer-Verlag, Berlin."},{"key":"383107_CR18","volume-title":"Technical Report","author":"M. Iri","year":"1994","unstructured":"Iri, M. (1994), An essay in the theory of uncontrollable flows and congestion. Technical Report, Department of Information and System Engineering, Faculty of Science and Engineering, Chuo University, TRISE 94\u201303."},{"key":"383107_CR19","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/978-0-387-34897-1_3","volume-title":"System Modelling and Optimization","author":"M. Iri","year":"1996","unstructured":"Iri, M. (1996), Network flow-theory and applications with practical impact. In J. Dole\u017eal and J. Fidler (eds.), System Modelling and Optimization, Chapman & Hall, London, 1996, pp. 24\u201336."},{"key":"383107_CR20","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0377-2217(88)90257-3","volume":"33","author":"H. Isermann","year":"1987","unstructured":"Isermann, H. and Steuer, E. (1987), Computational experience concerning payoff tables and minimum criterion values over the efficient set. European Journal of Operational Research 33, 91\u201397.","journal-title":"European Journal of Operational Research"},{"key":"383107_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-4098-4","volume-title":"Optimization on Low Rank Nonconvex Structures","author":"H. Konno","year":"1997","unstructured":"Konno, H., Thach, P.T. and Tuy, H. (1997), Optimization on Low Rank Nonconvex Structures. Kluwer, Dordrecht."},{"issue":"1","key":"383107_CR22","first-page":"67","volume":"25","author":"L.D. Muu","year":"2000","unstructured":"Muu, L.D. (2000), A convex-concave programming method for optimizing over the efficient set. Acta Mathematica Vietnamica 25(1), 67\u201385.","journal-title":"Acta Mathematica Vietnamica"},{"key":"383107_CR23","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/BF00932907","volume":"25","author":"P.H. Naccache","year":"1978","unstructured":"Naccache, P.H. (1978), Connectedness of the set of nondominated outcomes in multicriteria optimization. Journal of Optimization Theory and Applications 25, 459\u2013467.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383107_CR24","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF01584543","volume":"2","author":"J. Philip","year":"1972","unstructured":"Philip, J. (1972), Algorithms for the vector maximization problem. Mathematical Programming 2, 207\u2013229.","journal-title":"Mathematical Programming"},{"key":"383107_CR25","unstructured":"Phong, T.Q. and Tuyen, J.Q. (2000), Bisection search algorithm for optimizing over the efficient set. to appear in Vietman Journal of Mathematics."},{"key":"383107_CR26","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/0377-2217(88)90125-7","volume":"36","author":"G.R. Reeves","year":"1988","unstructured":"Reeves, G.R. and Reid, C. (1988), Minimum values over the efficient set in multiple objective decision making. European Journal of Operational Research 36, 334\u2013338.","journal-title":"European Journal of Operational Research"},{"key":"383107_CR27","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. and Wets, R.J-B. (1998), Variational Analysis. Springer, Berlin."},{"key":"383107_CR28","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0167-6377(95)00046-1","volume":"19","author":"S. Sayin","year":"1996","unstructured":"Sayin, S. (1996), An algorithm based on facial decomposition for finding the efficient set in multiple objective linear programming. Operations Research Letters 19, 87\u201392.","journal-title":"Operations Research Letters"},{"key":"383107_CR29","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1287\/opre.48.1.65.12449","volume":"48","author":"S. Sayin","year":"2000","unstructured":"Sayin, S. (2000), Optimizing over the efficient set using a top-down search of faces. Operations Research 48, 65\u201372.","journal-title":"Operations Research"},{"key":"383107_CR30","volume-title":"Theory ofMultiobjective Optimization","author":"Y. Sawaragi","year":"1985","unstructured":"Sawaragi, Y., Nakayama, H. and Tanino, T. (1985), Theory ofMultiobjective Optimization. Academic Press, Orland."},{"key":"383107_CR31","first-page":"271","volume":"22","author":"J.M. Shi","year":"1997","unstructured":"Shi, J.M. and Yamamoto, Y. (1997), A global optimization method for minimum maximal flow problem. Acta Mathematica Vietnamica 22, 271\u2013287.","journal-title":"Acta Mathematica Vietnamica"},{"key":"383107_CR32","volume-title":"Multiple Criteria Optimization: Theory, Computation and Application","author":"R.E. Steuer","year":"1985","unstructured":"Steuer, R.E. (1985), Multiple Criteria Optimization: Theory, Computation and Application. Wiley, New York."},{"key":"383107_CR33","volume-title":"Manual for the ADBASE multiple objective linear programming package","author":"R.E. Steuer","year":"1995","unstructured":"Steuer, R.E. (1995), Manual for the ADBASE multiple objective linear programming package. Department of Management Science and Information Technology, University of Georgia."},{"key":"383107_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-46216-0","volume-title":"Convexity and Optimization in Finite Dimensions","author":"J. Stoer","year":"1970","unstructured":"Stoer, J. and Witzgall, C. (1970), Convexity and Optimization in Finite Dimensions I. Springer-Verlag, Berlin."},{"key":"383107_CR35","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0022-247X(91)90197-8","volume":"159","author":"P.T. Thach","year":"1991","unstructured":"Thach, P.T. (1991), Quasiconjugates of functions, duality relationship between quasiconvex minimization under a reverse convex constraints and quasiconvex maximization under a cnvex constraint, and applications. Journal of Mathematical Analysis and Applications 159, 299\u2013322.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"383107_CR36","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1137\/0524087","volume":"24","author":"P.T. Thach","year":"1993","unstructured":"Thach, P.T., (1993), Global optimality criterion and a duality with a zero gap in nonconvex optimization. SIAM Journal on Mathematical Analysis 24, 1537\u20131556.","journal-title":"SIAM Journal on Mathematical Analysis"},{"key":"383107_CR37","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1137\/0804002","volume":"4","author":"P.T. Thach","year":"1994","unstructured":"Thach, P.T. (1994), A nonconvex duality with zero gap and applications. SIAM Journal on Optimization 4, 44\u201364.","journal-title":"SIAM Journal on Optimization"},{"key":"383107_CR38","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/BF02192205","volume":"88","author":"P.T. Thach","year":"1996","unstructured":"Thach, P.T., Konno, H. and Yokota, D. (1996), Dual approach to nminimization on the set of paretooptimal solutions. Journal of Optimization Theory and Applications 88, 689\u2013707.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383107_CR39","first-page":"21","volume":"8","author":"T.V. Thieu","year":"1983","unstructured":"Thieu, T.V., Tam, B.T. and Ban, V.T. (1983), An outer-approximation method for globally minimizing a concave function over a compact convex set. Acta Mathematica Vietnamica 8, 21\u201340.","journal-title":"Acta Mathematica Vietnamica"},{"key":"383107_CR40","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/S0377-2217(99)00068-5","volume":"122","author":"N.V. Thoai","year":"2000","unstructured":"Thoai, N.V. (2000), A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem. European Journal of Operational Research 122, 58\u201368.","journal-title":"European Journal of Operational Research"},{"key":"383107_CR41","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1023\/A:1026544116333","volume":"18","author":"N.V. Thoai","year":"2001","unstructured":"Thoai, N.V. (2001), Conical algorithm in global optimization for optimizing over efficient sets Journal of Global Optimization, 18, 321\u2013336.","journal-title":"Journal of Global Optimization"},{"key":"383107_CR42","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2809-5","volume-title":"Convex Analysis and Global Optimization","author":"H. Tuy","year":"1998","unstructured":"Tuy, H. (1998), Convex Analysis and Global Optimization. Kluwer, Dordrecht."},{"key":"383107_CR43","volume-title":"Optimality and Efficiency","author":"D.J. White","year":"1982","unstructured":"White, D.J. (1982), Optimality and Efficiency. John Wiley & Sons, Chichester."},{"key":"383107_CR44","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0377-2217(95)00184-0","volume":"94","author":"D.J. White","year":"1996","unstructured":"White, D.J. (1996), The maximization of a function over the efficient set via a penalty function approach, European Journal of Operational Research 94, 143\u2013153.","journal-title":"European Journal of Operational Research"},{"key":"383107_CR45","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1008336124425","volume":"16","author":"S. Yamada","year":"2000","unstructured":"Yamada, S., Tanino, T. and Inuiguchi, M. (2000), An inner approximation method for optimization over the weakly efficient set. Journal of Global Optimization 16, 197\u2013217.","journal-title":"Journal of Global Optimization"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1013875600711.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1013875600711\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1013875600711.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:38:14Z","timestamp":1751366294000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1013875600711"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":45,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["383107"],"URL":"https:\/\/doi.org\/10.1023\/a:1013875600711","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}