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

Tanino T (1985). Consideration on Supremum in a Multidimensional Space and Conjugate Duality in Multiobjective Optimization. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-85-081

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Abstract

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.

Item Type: Monograph (IIASA Working Paper)
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:55
Last Modified: 18 Nov 2016 19:18
URI: http://pure.iiasa.ac.at/2622

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