Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems

In this paper, we deal with robust optimal solution sets for a class of optimization problems with data uncertainty in both the objective and constraints. We first introduce a mixed-type robust dual problem of this class of uncertain optimization problems and explore robust strong duality relations...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2019-09, Vol.182 (3), p.984-1000
Main Authors: Sun, Xiangkai, Teo, Kok Lay, Tang, Liping
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Robustness (mathematics)
Theory of Computation
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Summary:In this paper, we deal with robust optimal solution sets for a class of optimization problems with data uncertainty in both the objective and constraints. We first introduce a mixed-type robust dual problem of this class of uncertain optimization problems and explore robust strong duality relations between them. Then, we propose a new approach to characterize robust optimal solution sets of this class of uncertain optimization problems via its dual problem. Moreover, we show that several results on characterizations of robust optimal solution sets of uncertain optimization problems obtained in recent literature can be obtained using our approach.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-019-01496-w