

1 预备知识


2 双约束二阶锥变分不等式的等价转换

3 一阶必要性条件




4 二阶充分性条件

Journal of Shenyang Aerospace University >
Optimality condition analysis of the second-order cone coupled constrained variational inequalities
Received date: 2023-03-31
Online published: 2023-11-09
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.
WANG Bin , WANG Li , SUN Juhe , SUN Yining , YUAN Yanhong . Optimality condition analysis of the second-order cone coupled constrained variational inequalities[J]. Journal of Shenyang Aerospace University, 2023 , 40(4) : 60 -66 . DOI: 10.3969/j.issn.2095-1248.2023.04.008
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