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

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.

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

Key words

second-order cone constrained / variational inequality / Karush-Kuhn-Tucker condition / Robinson constraint specification / first-order necessity condition / second-order sufficiency condition

基金资助

国家自然科学基金(11901422)