向量值映射的恰当锥拟凸性和锥半连续性的刻画

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向量值映射的恰当锥拟凸性和锥半连续性的刻画李飞¹, 杨新民²1. 内蒙古大学数学科学学院, 呼和浩特 010021;
2. 重庆师范大学数学科学学院, 重庆 400047 Characterizations of Proper Cone Quasiconvexity and Cone Semicontinuity via Nonlinear Scalarization Functions for Vector-valued Maps LI Fei¹, YANG Xinmin²1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China

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摘要首先讨论了一个非线性标量化函数的基本性质并给出了其对偶形式.在此基础上建立了对向量值映射的恰当锥拟凸性的刻画.然后提出了锥形邻域的概念并给出了向量值映射的一类新的锥半连续性的统一定义.最后通过两个非线性标量化函数得到了对向量值映射的锥半连续性的完整刻画.

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收稿日期: 2019-02-01

PACS:

O221.6

基金资助:国家自然科学基金（11601248，11431004）资助项目.

引用本文:

李飞, 杨新民. 向量值映射的恰当锥拟凸性和锥半连续性的刻画[J]. 应用数学学报, 2021, 44(5): 646-658. LI Fei, YANG Xinmin. Characterizations of Proper Cone Quasiconvexity and Cone Semicontinuity via Nonlinear Scalarization Functions for Vector-valued Maps. Acta Mathematicae Applicatae Sinica, 2021, 44(5): 646-658.

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http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2021/V44/I5/646

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