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: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Taylor & Francis
03.03.2024
Taylor & Francis LLC |
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| ISSN: | 0233-1934, 1029-4945 |
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| Abstract | 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. |
|---|---|
| AbstractList | In this article, we employ advanced techniques of convex analysis and 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 C denotes the set of all 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 C-derivatives of uncertain constraint functions. We second establish KKT-type robust necessary conditions for robust (weakly) efficient solutions via the subdifferentials of C-derivatives to such problems. We third propose two new kinds of generalized C-convex functions via the subdifferentials of C-derivatives involving max-functions. Under suitable assumptions on the generalized 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. 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. |
| Author | Su, Tran Van Linh, Dang Hong Nguyen, Thuy Thi Thu |
| Author_xml | – sequence: 1 givenname: Thuy Thi Thu surname: Nguyen fullname: Nguyen, Thuy Thi Thu organization: School of Applied Mathematics and Informatics, Hanoi University of Science and Technology – sequence: 2 givenname: Tran Van surname: Su fullname: Su, Tran Van email: tvsu@ued.udn.vn, sutrantud@gmail.com organization: Department of Mathematics, The University of Danang - University of Science and Education – sequence: 3 givenname: Dang Hong surname: Linh fullname: Linh, Dang Hong organization: School of Applied Mathematics and Informatics, Hanoi University of Science and Technology |
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$ \mathcal {C} $
C
-differentiation to examine KKT-type robust necessary and sufficient... In this article, we employ advanced techniques of convex analysis and C-differentiation to examine KKT-type robust necessary and sufficient optimality... |
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| SubjectTerms | 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 |
| Title | Robust optimality conditions for multiobjective programming problems under data uncertainty and its applications |
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