具有双约束条件的变分不等式的二阶微分方程方法
The Second-Order Differential Equation Method for Variational Inequality with Cou-pling Constraints
DOI: 10.12677/PM.2022.125092, PDF,    国家自然科学基金支持
作者: 陈星旭, 王 莉, 孙菊贺：沈阳航空航天大学理学院，辽宁 沈阳；杨 峥：辽宁省实验学校数学教研组，辽宁 沈阳
关键词: 变分不等式；微分方程方法；拉格朗日函数；投影算子；Variational Inequality； Differential Equation Method； Lagrange Function； Projection Operator
摘要: 本文研究的主要内容是具有双约束条件的变分不等式问题。将具有双约束条件的变分不等式看作一类特殊的优化问题，运用该优化问题的拉格朗日函数的鞍点不等式和投影算子，建立了具有控制过程的二阶微分方程系统，并证明了该微分方程系统的解的轨迹的聚点是具有双约束条件的变分不等式的解。最后，运用具有控制过程的二阶微分方程系统求解了两个算例，该数值结果验证了该方法的有效性。
Abstract: In this paper, we consider the second-order differential equation method for solving the variational inequality with coupling constraints. The variational inequality with coupling constraints is regarded as a special optimization problem. Using the saddle point inequality and projection op-erator of Lagrange function, the second-order differential equation system with control process is established, and it is proved that the convergence point of the solution trajectory of this differential equation system is the solution of the variational inequality with coupling constraints. Finally, two numerical examples are solved by using the second-order differential equation system with control process, and the numerical results verify the effectiveness of this method.
文章引用：陈星旭, 王莉, 孙菊贺, 杨峥. 具有双约束条件的变分不等式的二阶微分方程方法[J]. 理论数学, 2022, 12(5): 814-825. https://doi.org/10.12677/PM.2022.125092

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