双约束二阶锥变分不等式的最优性条件分析

王彬; 王莉; 孙菊贺; 孙艺宁; 袁艳红

doi:10.3969/j.issn.2095-1248.2023.04.008

沈阳航空航天大学学报 ›› 2023, Vol. 40 ›› Issue (4) : 60 -66. DOI: 10.3969/j.issn.2095-1248.2023.04.008

基础科学和工程

双约束二阶锥变分不等式的最优性条件分析

王彬 ¹ ,
王莉 ¹ ,
孙菊贺 ¹ ,
孙艺宁 ¹ ,
袁艳红 ²

作者信息 +

Optimality condition analysis of the second-order cone coupled constrained variational inequalities

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

Author information +

文章历史 +

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摘要

为研究双约束二阶锥变分不等式问题的最优性条件，通过对原始问题进行等价转换后，借助所得出的广义鞍点问题，建立极小极大问题模型，将其等价为变分不等式组问题，得到该变分不等式组对应的karush-kuhn-tucker （简记为KKT）条件。进一步应用Lagrange对偶理论推导出所研究的双约束二阶锥变分不等式问题的一阶必要性条件。基于约束集合的切锥、二阶切集公式及对偶理论，可以推导出双约束二阶锥变分不等式问题的二阶充分性条件。双约束二阶锥变分不等式问题的最优性条件分析对该问题解的存在性及收敛性研究给出了理论支持。

Abstract

In order to study the optimality conditions of the second order cone coupled constrained variational inequalities， after equivalent transformation of the original problem， a minimax problem model was established by using the generalized saddle point problem， which was equivalent to a system of variational inequalities problem. The karush-kuhn-tucker （abbreviated as KKT） conditions of this system of variational inequalities were obtained. The Lagrange duality theory was applied to obtain the first-order necessity condition for the second-order cone coupled constrained variational inequalities. Based on the tangent cone of the constrained sets， the formula of the second-order tangent set and the duality theory， the second-order sufficiency condition of the second-order cone coupled constrained variational inequalities was derived. The analysis of the optimality condition for the second-order cone coupled constrained variational inequalities provides theoretical support for the study of the existence and convergence of the solution to the second-order cone coupled constrained variational inequalities.