Journal
OPTIMIZATION
Volume 69, Issue 3, Pages 493-518Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2019.1625352
Keywords
Uncertain multiobjective optimization; image space analysis; robustness; robust optimality conditions; vectorization counterparts
Funding
- National Natural Science Foundation of China [11301567, 11571055]
- Fundamental Research Funds for the Central Universities [106112017CDJZRPY0020]
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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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