工程数学学报
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张亚萌, 余国林
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ZHANG Ya-meng, YU Guo-lin
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摘要： 本文研究向量变分不等式与非光滑多目标优化问题高阶严格极小解之间的关系．首先，引入了一类广义高阶强伪凸Lipschitz函数的概念，称之为高阶强伪凸type I函数，并且给出具体实例说明其存在性．其次，在高阶强伪凸type I函数假设下，给出了高阶严格极小元，向量关键点和弱向量变分不等式解之间的关系刻画．
关键词: 多目标优化, 高阶严格极小解, 向量变分不等式, 强凸性
Abstract: This paper is devoted to the study of the relations between vector variational inequality and nonsmooth multi-objective optimization in the sense of strict minimizers of higher order. We firstly introduce an extension of higher-order strong pseudoconvexity for Lipschitz functions, termed higher-order strongly pseudoconvex functions of type I, and some examples are presented in the support of this generalization. Then, we identify the strict minimizers of higher order, the vector critical points and the solutions of the weak vector variational inequality problem under the higher-order strong pseudoconvexity of type I hypothesis. It is our understanding that such results have not been established till now.
Key words: multi-objective optimization, strict minimizer of higher order, vector variational inequality, strong convexity
中图分类号:
O212.7
张亚萌, 余国林. 向量变分不等式和多目标优化高阶严格极小解的关系（英）[J]. 工程数学学报, doi: 10.3969/j.issn.1005-3085.2021.03.013.
ZHANG Ya-meng, YU Guo-lin. Relationships between Vector Variational Inequality and Multi-objective Optimization for Strict Minimizer of Higher Order[J]. Chinese Journal of Engineering Mathematics, doi: 10.3969/j.issn.1005-3085.2021.03.013.
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链接本文: http://jgsx-csiam.org.cn/CN/10.3969/j.issn.1005-3085.2021.03.013
http://jgsx-csiam.org.cn/CN/Y2021/V38/I3/441
