Asymptotic Characterization of Non-Emptiness and Boundedness of Efficient Solution Sets for Nonconvex Multi-Objective Optimization Problems

LIU Ying; FU Xiaoheng; TANG Liping

doi:10.21656/1000-0887.450235

Volume 46 Issue 4

Apr. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(4): 519-527

LIU Ying, FU Xiaoheng, TANG Liping. Asymptotic Characterization of Non-Emptiness and Boundedness of Efficient Solution Sets for Nonconvex Multi-Objective Optimization Problems[J]. Applied Mathematics and Mechanics, 2025, 46(4): 519-527. doi: 10.21656/1000-0887.450235

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Asymptotic Characterization of Non-Emptiness and Boundedness of Efficient Solution Sets for Nonconvex Multi-Objective Optimization Problems

doi: 10.21656/1000-0887.450235

LIU Ying^1
,,
FU Xiaoheng^2
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TANG Liping^{2
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1.
School of Mathematical Sciences, Chongqing Normal University, Chonging 401331, P.R.China
2.
National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chonging 401331, P.R.China

Received Date: 2024-08-22
Rev Recd Date: 2024-09-26
Publish Date: 2025-04-01

Abstract

Abstract

The non-emptiness and boundedness of the solution sets of optimization problems play a crucial role in numerical algorithms. Based on asymptotic analysis, the non-emptiness and boundedness of the (proper) efficient solution sets for nonconvex multi-objective optimization problems under regularity conditions were obtained. Firstly, the inner and outer asymptotic estimations were established for the efficient solution sets and the properly efficient solution sets of nonconvex multi-objective optimization problems via asymptotic cones and asymptotic functions. Then, based on these estimates, the non-emptiness and boundedness of the efficient solution sets for nonconvex multi-objective optimization problems were characterized. Finally, some necessary conditions for the existence of efficient solutions to nonconvex multi-objective optimization problem were given.
- nonconvex multi-objective optimization,
- efficient solution,
- regularity,
- asymptotic cone,
- asymptotic function

Recommended by YANG Xinmin, M.AMM Editorial Board

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References

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