Characterizations of multiobjective robustness on vectorization counterparts

In this paper, we characterize robust solutions for uncertain multiobjective optimization problems on the basis of vectorization models by virtue of image space analysis. By introducing corrected image of original uncertain problem or the selected and corrected images of its robust counterpart, an e...

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Bibliographic Details
Published in:Optimization Vol. 69; no. 3; pp. 493 - 518
Main Authors: Wei, Hong-Zhi, Chen, Chun-Rong, Li, Sheng-Jie
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.03.2020
Taylor & Francis LLC
Subjects:
image space analysis
Mathematical programming
Multiple objective analysis
Nonlinear programming
Optimization
robust optimality conditions
Robustness
Separation
Uncertain multiobjective optimization
vectorization counterparts
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this paper, we characterize robust solutions for uncertain multiobjective optimization problems on the basis of vectorization models by virtue of image space analysis. By introducing corrected image of original uncertain problem or the selected and corrected images of its robust counterpart, an equivalent relation between multiobjective robustness and the separation of two sets in the image space is well established. Moreover, by means of linear (vector/scalar) separation functions, some Lagrangian-type sufficient robust optimality conditions are presented. Especially, under suitable restriction assumptions, we derive Lagrangian-type necessary robust optimality conditions in terms of nonlinear separation functions. These results obtained in this paper extend and improve some existing ones recently. Finally, several examples are given to show the effectiveness of the conclusions.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2019.1625352