Robust optimality conditions for multiobjective programming problems under data uncertainty and its applications

In this article, we employ advanced techniques of convex analysis and $ \mathcal {C} $ C -differentiation to examine KKT-type robust necessary and sufficient optimality conditions and robust duality for an uncertain multiobjective programming problem under uncertainty sets, where $ \mathcal {C} $ C...

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Published in:Optimization Vol. 73; no. 3; pp. 641 - 672
Main Authors: Nguyen, Thuy Thi Thu, Su, Tran Van, Linh, Dang Hong
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.03.2024
Taylor & Francis LLC
Subjects:
Convex analysis
Convexity
Derivatives
duality theorems
KKT-type robust optimality conditions
mathcal {C}
Mathematical programming
Multiobjective programming problem with uncertain data
Multiple objective analysis
Robustness (mathematics)
Uncertainty
uncertainty sets
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this article, we employ advanced techniques of convex analysis and $ \mathcal {C} $ C -differentiation to examine KKT-type robust necessary and sufficient optimality conditions and robust duality for an uncertain multiobjective programming problem under uncertainty sets, where $ \mathcal {C} $ C denotes the set of all $ \mathcal {G} $ G -derivatives which are positively homogeneous and convex with respect to the second argument. We first provide the robust constraint qualification of the (RCQ) type via the $ \mathcal {C} $ C -derivatives of uncertain constraint functions. We second establish KKT-type robust necessary conditions for robust (weakly) efficient solutions via the subdifferentials of $ \mathcal {C} $ C -derivatives to such problems. We third propose two new kinds of generalized $ \mathcal {C} $ C -convex functions via the subdifferentials of $ \mathcal {C} $ C -derivatives involving max-functions. Under suitable assumptions on the generalized $ \mathcal {C} $ C -convexity, KKT-type robust necessary optimality conditions become robust sufficient optimality conditions. Furthermore, we formulate as some applications a dual multiobjective programming problem to the underlying programming and examine weak, strong, and converse duality theorems for the same. Some illustrative examples are also provided for our findings.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2122717