孙艺宁(1998-),女,辽宁辽阳人,硕士研究生,主要研究方向:运筹学与控制论,E-mail: yiningsun527@163.com |
王莉(1978-),女,辽宁葫芦岛人,副教授,博士,主要研究方向:运筹学与控制论,E-mail:liwang211@163.com。 |
收稿日期: 2022-12-05
网络出版日期: 2023-11-09
基金资助
国家自然科学基金(11901422)
Optimality conditions for the second-order cone constrained variational inequalities
Received date: 2022-12-05
Online published: 2023-11-09
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。
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
孙艺宁 , 王莉 , 孙菊贺 , 王彬 , 袁艳红 . 二阶锥约束变分不等式的最优性条件[J]. 沈阳航空航天大学学报, 2023 , 40(4) : 67 -71 . DOI: 10.3969/j.issn.2095-1248.2023.04.009
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.
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齐爽.两阶段随机二阶锥规划问题的最优性条件[D].大连:辽宁师范大学,2020.
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