二阶锥约束变分不等式的最优性条件  

Optimality conditions for the second-order cone constrained variational inequalities

作　　者：孙艺宁 王莉 孙菊贺 王彬 袁艳红[2] SUN Yining;WANG Li;SUN Juhe;WANG Bin;YUAN Yanhong(College of Science,Shenyang Aerospace University,Shenyang 110136,China;College of Economics and Management,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]沈阳航空航天大学理学院,沈阳110136 [2]太原理工大学经济管理学院,太原030024

出　　处：《沈阳航空航天大学学报》2023年第4期67-71,共5页Journal of Shenyang Aerospace University

基　　金：国家自然科学基金(项目编号:11901422)。

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。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 secondorder 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.

关 键 词：二阶锥约束 变分不等式 Karush-Kuhn-Tucker条件 Robinson约束规范 一阶必要性条件 二阶充分性条件 

分 类 号：O224[理学—运筹学与控制论]