Consideration on Supremum in a Multidimensional Space and Conjugate Duality in Multiobjective Optimization

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/2671 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/2671 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/2671 archive 351 disk0/00/00/26/22 2016-01-15 01:55:47 2021-08-27 17:12:18 2016-01-15 01:55:47 monograph show 2 Tanino T. AL1287 Consideration on Supremum in a Multidimensional Space and Conjugate Duality in Multiobjective Optimization pub iis_met prog_sds The first part of this paper is devoted to consideration on the definition of "supremum" in a multi-dimensional Euclidean space. A desirable definition is looked for among several possible alternatives. In the second part conjugate duality in multiobjective optimization is developed. Supremum is defined in the extended multi-dimensional Euclidean space on the basis of consideration in the first part. Some useful concepts such as conjugate maps and subgradients are introduced for vector-valued set-valued maps. Finally a strong duality result for a multiobjective optimization problem is proved under a regularity condition. 1985-12 published WP-85-081 WP-85-081 2445 public working_paper IIASA, Laxenburg, Austria 31 FALSE info:eu-repo/semantics/book