Hadamard Well-Posedness in 2 Types of Set Optimization Problems

CHENG Xiang; PENG Zaiyun; YANG Xin; WEN Ming

doi:10.21656/1000-0887.450273

Volume 46 Issue 7

Jul. 2025

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CHENG Xiang, PENG Zaiyun, YANG Xin, WEN Ming. Hadamard Well-Posedness in 2 Types of Set Optimization Problems[J]. Applied Mathematics and Mechanics, 2025, 46(7): 926-938. doi: 10.21656/1000-0887.450273

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Hadamard Well-Posedness in 2 Types of Set Optimization Problems

doi: 10.21656/1000-0887.450273

School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Received Date: 2024-10-15
Rev Recd Date: 2025-06-08

Available Online: 2025-07-30

Publish Date: 2025-07-01

Abstract

Abstract

The Hadamard well-posedness of a set optimization problem (P) and an infinite set optimization problem (ISOP) under upper set order relation was studied. Firstly, in the case of the gamma convergence of the set-valued mapping sequence, the definitions of the generalized Hadamard well-posedness and the ε-generalized Hadamard well-posedness for (P) were given, the relationship between these 2 types of well-posednesses were established, and the sufficient conditions for the Hadamard well-posedness of (P) were obtained. Then the sufficient conditions for the Hadamard well-posedness of (ISOP) were studied with the concept of Hausdorff cone-continuity under functional perturbations of both constraint sets and objective maps. The results improve those in the relevant previous references, enriching the study of set optimization problems.
- set optimization problem,
- Hadamard well-posedness,
- Gamma-convergence,
- Hausdorff cone-continuity

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References

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