二阶锥约束变分不等式的最优性条件

孙艺宁; 王莉; 孙菊贺; 王彬; 袁艳红

doi:10.3969/j.issn.2095-1248.2023.04.009

沈阳航空航天大学学报 ›› 2023, Vol. 40 ›› Issue (4) : 67 -71. DOI: 10.3969/j.issn.2095-1248.2023.04.009

基础科学和工程

二阶锥约束变分不等式的最优性条件

孙艺宁 ¹ ,
王莉 ¹ ,
孙菊贺 ¹ ,
王彬 ¹ ,
袁艳红 ²

作者信息 +

Optimality conditions for the second-order cone constrained variational inequalities

Yining SUN ¹ ,
Li WANG ¹ ,
Juhe SUN ¹ ,
Bin WANG ¹ ,
Yanhong YUAN ²

Author information +

文章历史 +

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摘要

研究了二阶锥约束变分不等式的最优性条件。首先，将二阶锥约束变分不等式转化为特殊的极小化问题，得到了二阶锥约束变分不等式问题的等价形式；其次，根据等价形式得到了二阶锥约束变分不等式问题的一阶必要性条件；最后，证明了满足Robinson约束规范的二阶充分性条件。该最优性条件的分析为二阶锥约束变分不等式的算法设计提供了理论支撑。

Abstract

The optimality conditions for the second-order cone constrained variational inequalities was studied.Firstly，the second-order cone constrained variational inequalities were transformed into a special minimization problem，and the equivalent form for the second-order cone constrained variational inequalities was obtained.Secondly，the first-order necessity conditions for the second-order cone constrained variational inequalities was obtained according to the equivalent form.Finally，the second-order sufficiency condition satisfying Robinson constraint specification was proved.The analysis of optimality conditions provides the oretical support for the algorithm design of the second-order cone constrained variational inequalities.