Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces

Saadati, Maryam; Oveisiha, M.

doi:10.36045/j.bbms.210705

Cited by 7 publications

(2 citation statements)

References 17 publications

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“…Recently, some different concepts of robustness used in multiobjective optimization in the face of data uncertainty have been established in [7,8,14,20,28].…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions for robust multiobjective optimization programming in Asplund spaces

Saadati,

Oveisiha

2022

Preprint

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In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust efficient solutions and then establish necessary optimality theorem for approximate weakly robust quasi-efficient solutions of the problem in the sense of the limiting subdifferential by exploiting a fuzzy optimality condition in terms of the Fréchet subdifferential. Sufficient conditions for approximate (weakly) robust quasi-efficient solutions to such a problem are also driven under the new concept of generalized pseudo convex functions. Finally, we address an approximate Mond-Weir-type dual robust problem to the reference problem and explore weak, strong, and converse duality properties under assumptions of pseudo convexity.

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“…Recently, some different concepts of robustness used in multiobjective optimization in the face of data uncertainty have been established in [7,8,14,20,28].…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions for robust multiobjective optimization programming in Asplund spaces

Saadati,

Oveisiha

2022

Preprint

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“…and F and G are identical maps, the problem (CUP) collapses to the following uncertain multiobjective optimization problem stated bySaadati and Oveisiha (2022b) …”

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Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

Saadati,

Oveisiha

2023

Preprint

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This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields ((CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of (CUP) in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond-Weir-type robust dual problem to the primal problem (CUP), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.

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Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

Saadati,

Oveisiha

2024

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Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces

Cited by 7 publications

References 17 publications

Approximate solutions for robust multiobjective optimization programming in Asplund spaces

Approximate solutions for robust multiobjective optimization programming in Asplund spaces

Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

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