Journal Article10.1007/S11228-006-0028-2
Conic Set-Valued Maps in Vector Optimization
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TL;DR: In this article, the authors deal with the properties of a conic set-valued function defined on the set of all ideal points of vector programming problems and prove that certain contingent cones are determined by the ideal conic map.
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Abstract: The paper deals with the properties of a conic set-valued function defined on the set of all ideal points of vector programming problems. The results here about the continuity and derivability of this conic set-valued map, can be used to get information about the sensitivity of the problem and the stability of the order associated to every ideal point. Furthermore, it is proved that certain contingent cones are determined by the ideal conic set-valued map.
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Citations
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Polar Conic Set-Valued Map in Vector Optimization. Continuity and Derivability
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Optimality Conditions for Vector Optimization Problems
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- 01 Jan 2014
TL;DR: In this article, the authors provide subdifferential information for the scalarization functionals introduced in Chap. 6 and formulate necessary and sufficient optimality conditions of Fermat and Lagrange type for unconstrained and constrained vector optimization problems with (set-valued) objective maps mapping in a real linear space equipped with a variable ordering structure.
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Yoshikazu Sawaragi,Tetsuzo Tanino,Hirotaka Nakayama +2 more
- 12 Oct 1985
1.5K
Compromise Solutions, Domination Structures, and Salukvadze’s Solution
Po-Lung Yu,George Leitmann +1 more
TL;DR: In this paper, the concepts of compromise solutions and domination structures are discussed in such a way that the underlying assumptions and their implications concerning the solution concept suggested by Salukvadze may be clearer.
175
Duality, Indifference and Sensitivity Analysis inr Multiple Objective Linear Programming
TL;DR: The duality of such programmes is investigated, and the duality theorem is used to illustrate aspects of sensitivity analysis with multiple objectives.
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