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非凸多目标优化问题有效解集的非空性有界性的渐近刻画

刘应 傅小恒 唐莉萍

刘应, 傅小恒, 唐莉萍. 非凸多目标优化问题有效解集的非空性有界性的渐近刻画[J]. 应用数学和力学, 2025, 46(4): 519-527. doi: 10.21656/1000-0887.450235
引用本文: 刘应, 傅小恒, 唐莉萍. 非凸多目标优化问题有效解集的非空性有界性的渐近刻画[J]. 应用数学和力学, 2025, 46(4): 519-527. doi: 10.21656/1000-0887.450235
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
Citation: 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

非凸多目标优化问题有效解集的非空性有界性的渐近刻画

doi: 10.21656/1000-0887.450235
基金项目: 

国家自然科学基金(面上项目)(12171060)

重庆市教委重大项目(KJZDM202300504)

国家自然科学基金(重大项目)(11991024)

重庆市自然科学基金(ncamc2022msxm01

CSTB2024NSCQLZX0140)

详细信息
    作者简介:

    刘应(1997—), 女, 硕士生(E-mail: 623032146@qq.com);傅小恒(1999—), 男, 硕士生(E-mail: 1352886841@qq.com);唐莉萍(1985—), 女, 教授, 博士(通讯作者. E-mail: tanglipings@163.com).

    通讯作者:

    唐莉萍1985—), 女, 教授, 博士(通讯作者. E-mail: tanglipings@163.com).

  • 中图分类号: O221.6

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

Funds: 

The National Science Foundation of China(11991024)

  • 摘要: 优化问题解集的非空性和有界性在数值算法研究中发挥着重要作用.该文利用渐近分析工具, 在正则性条件下研究了非凸多目标优化问题有效解集的非空性和有界性.首先, 在正则条件下, 建立了非凸多目标优化问题的有效解集和真有效解集的内外渐近估计;然后, 根据这些估计, 获得了非凸多目标优化问题有效解集的非空有界性的渐近刻画;最后, 给出了非凸多目标优化问题有效解存在的必要条件.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2024-08-22
  • 修回日期:  2024-09-26
  • 网络出版日期:  2025-04-30

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