Stability of solution set mapping for parametric set-valued optimization problems via improved sets

MENG Xudong

doi:10.13471/j.cnki.acta.snus.2020A043

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Stability of solution set mapping for parametric set-valued optimization problems via improved sets

Research articles | 更新时间：2023-11-01

- Stability of solution set mapping for parametric set-valued optimization problems via improved sets
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 2, Pages: 180-188(2022)
- 作者机构：
  
  南昌航空大学科技学院，江西共青城 332020
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020A043
  CLC： O221.3
- Published：25 March 2022，
  
  Published Online：02 June 2021，
  
  Received：15 August 2020，
  
  Accepted：17 December 2020
扫描看全文
孟旭东.基于改进集的参数集值优化问题解集映射的稳定性[J].中山大学学报(自然科学版),2022,61(02):180-188.

MENG Xudong.Stability of solution set mapping for parametric set-valued optimization problems via improved sets[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(02):180-188.
孟旭东.基于改进集的参数集值优化问题解集映射的稳定性[J].中山大学学报(自然科学版),2022,61(02):180-188. DOI： 10.13471/j.cnki.acta.snus.2020A043.

MENG Xudong.Stability of solution set mapping for parametric set-valued optimization problems via improved sets[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(02):180-188. DOI： 10.13471/j.cnki.acta.snus.2020A043.

摘要

在实赋范线性空间中讨论了基于改进集的参数集值优化问题解集映射的稳定性。在目标函数具有

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1.94733346

2.28600001

-Hausdorff连续性和

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1.94733346

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-闭性及可行集具有连续性和紧凸性条件下，分析了关于改进集

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1.94733346

2.28600001

的水平集值映射的上半连续性和下半连续性。在此基础上，在目标函数构成的序偶映射具有严格

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1.94733346

2.28600001

-拟凸性基本假设下，通过分析的方法获得了具改进集的参数集值优化问题解集映射的Berge连续性、Hausdorff连续性、

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1.94733346

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-Hausdorff连续性和紧闭性定理。

Abstract

The stability of solution set mapping for parameter set-valued optimization problems via improved sets in real normed vector space is discussed. The upper semi-continuity and lower semi-continuity of level set-valued mappings via improved sets

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is analyzed under the conditions that the objective function having

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2.53999996

2.62466669

-Hausdorff continuity and

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2.28600001

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-closure and the feasible set having continuity and compact convexity. On this basis， through the method of analysis， the theorems of the Berge continuity， Hausdorff continuity，

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2.53999996

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-Hausdorff continuity compactness and closeness of solution set mapping for parametric set-valued optimization problems via improved sets are obtained by the method of analysis with the help of the basic assumption of strict-quasi-convexity for the ordered-even mappings composed of objective functions.

关键词

解集映射改进集稳定性连续性参数集值优化问题

Keywords

solution set mappingimproved setsstabilitycontinuityparameter set-valued optimization problems

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