caa a22 4500 463169204 CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s10957-007-9219-8 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9219-8 On Optimization over the Efficient Set in Linear Multicriteria Programming [Elektronische Daten] [R. Horst, N. Thoai, Y. Yamamoto, D. Zenke] The efficient set of a linear multicriteria programming problem can be represented by a reverse convex constraint of the form g(z)≤0, where g is a concave function. Consequently, the problem of optimizing some real function over the efficient set belongs to an important problem class of global optimization called reverse convex programming. Since the concave function used in the literature is only defined on some set containing the feasible set of the underlying multicriteria programming problem, most global optimization techniques for handling this kind of reverse convex constraint cannot be applied. The main purpose of our article is to present a method for overcoming this disadvantage. We construct a concave function which is finitely defined on the whole space and can be considered as an extension of the existing function. Different forms of the linear multicriteria programming problem are discussed, including the minimum maximal flow problem as an example. Springer Science+Business Media, LLC, 2007 Multicriteria optimization nationallicence Optimization over the efficient set nationallicence Global optimization nationallicence Reverse convex constraint nationallicence Minimum maximal flow problem nationallicence Horst R. Department of Mathematics, University of Trier, 54286, Trier, Germany aut Thoai N. Department of Mathematics, University of Trier, 54286, Trier, Germany aut Yamamoto Y. Graduate School of Systems and Information Engineering, University of Tsukuba, 305-8573, Tsukuba, Japan aut Zenke D. Graduate School of Systems and Information Engineering, University of Tsukuba, 305-8573, Tsukuba, Japan aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 433-443 0022-3239 134:3<433 2007 134 10957 https://doi.org/10.1007/s10957-007-9219-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9219-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Horst R. Department of Mathematics, University of Trier, 54286, Trier, Germany aut NATIONALLICENCE 700 1- Thoai N. Department of Mathematics, University of Trier, 54286, Trier, Germany aut NATIONALLICENCE 700 1- Yamamoto Y. Graduate School of Systems and Information Engineering, University of Tsukuba, 305-8573, Tsukuba, Japan aut NATIONALLICENCE 700 1- Zenke D. Graduate School of Systems and Information Engineering, University of Tsukuba, 305-8573, Tsukuba, Japan aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 433-443 0022-3239 134:3<433 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer