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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 98-110.doi: 10.6040/j.issn.1671-9352.0.2020.343

• • 上一篇    

集合优化问题解集的稳定性和扩展适定性

孟旭东   

  1. 南昌航空大学科技学院, 江西 共青城 332020
  • 发布日期:2022-01-07
  • 作者简介:孟旭东(1982— ),男,硕士,副教授,研究方向为向量均衡与向量优化理论及其应用. E-mail:mxudongm@163.com
  • 基金资助:
    江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614);江西省教育厅科学技术研究项目(GJJ161597,GJJ218701)

Stability and extended well-posedness of the solution sets for set optimization problems

MENG Xu-dong   

  1. Science and Technology College of Nanchang Hangkong University, Gongqingcheng 332020, Jiangxi, China
  • Published:2022-01-07

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摘要： 研究了集合优化问题近似解集的稳定性和扩展适定性。当目标函数具连续性和广义锥-拟凸性时,讨论了集合优化问题近似解集的Painlevé-Kuratowski上收敛和下收敛。结合适当假设条件,分析了集合优化问题的扩展适定性和弱扩展适定性。

关键词: 集合优化问题, Painlevé-Kuratowski收敛, 稳定性, 扩展适定性

Abstract: The stability and extended well-posedness of the approximate solution sets for set optimization problems are studied. The Painlevé-Kuratowski upper convergence and lower convergence of the approximate solution sets for set optimization problems are discussed by assuming the continuity and generalized cone quasi-convexity of objective function. The extended well-posedness and weak extended well-posedness for set optimization problems are analyzed under some appropriate assumptions.

Key words: set optimization problem, Painlevé-Kuratowski convergence, stability, extended well-posedness

中图分类号: 

  • O221.3
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