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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (5): 843-850.doi: 10.3969/j.issn.1005-3085.2023.05.012

• • 上一篇    

广义二阶不变凸向量变分类不等式

高  鎏,  余国林,  王美美   

  1. 北方民族大学数学与信息科学学院，银川 750021
  • 收稿日期:2021-03-18 接受日期:2022-08-12 出版日期:2023-10-15 发布日期:2023-12-15
  • 通讯作者: 余国林 E-mail: guolin_yu@126.com
  • 基金资助:
    国家自然科学基金(11861002)；北方民族大学研究生创新项目(YCX23081).

Variational-like Inequalities Involving Generalized Second-order Invexities

GAO Liu,  YU Guolin,  WANG Meimei   

  1. School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021
  • Received:2021-03-18 Accepted:2022-08-12 Online:2023-10-15 Published:2023-12-15
  • Contact: G. Yu. E-mail address: guolin_yu@126.com}
  • Supported by:
    The National Natural Science Foundation of China (11861002); the Postgraduate Innovation Project of North Minzu University (YCX23081).

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摘要：

研究了广义二阶不变凸向量变分类不等式问题解的存在性，并讨论其与多目标优化问题解之间的关系。引入了两种广义二阶不变凸函数和一种广义二阶单调函数，并给出具体实例说明了它们的存在性。在广义二阶不变凸性假设下，利用分析的方法给出了向量变分类不等式与多目标优化问题解之间的关系。利用KKM定理，在广义二阶单调性假设下得到了向量变分类不等式问题解的存在性定理。研究表明在广义二阶单调性假设下，向量变分类不等式存在解，并且在适当的广义二阶凸性条件下，其解与多目标优化问题解之间相互等价。

关键词: 向量变分类不等式, 广义二阶不变凸性, KKM定理, 多目标优化

Abstract:

The existences of solutions to the generalized second-order invex vector variational-like inequality are investigated, and their relationships with those of multi-objective optimization problems are disclosed. Two classes of generalized second-order invex functions and a type of second-order monotone functions are introduced, some specific examples are presented to illustrate their existences. The relationships with respect to the solutions between vector variational-like inequalities and multi-objective optimization problems are established by using analytical method. Based on KKM theorem, the existence results of vector variational-like inequalities are obtained under the assumptions of the introduced second-order monotonicity. It is shown that the solutions of vector variational-like inequalities are existed and it exists the closely relationships with multi-objective optimization problems under the appropriate conditions.

Key words: vector variational-like inequality, generalized second-order invexity, KKM theorem, multi-objective optimization

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