增广Lagrange方法求解二阶锥约束变分不等式问题

刘雨; 孙菊贺; 王莉; 米娜; 袁艳红

doi:10.3969/j.issn.2095-1248.2023.04.010

沈阳航空航天大学学报 ›› 2023, Vol. 40 ›› Issue (4) : 72 -79. DOI: 10.3969/j.issn.2095-1248.2023.04.010

基础科学和工程

增广Lagrange方法求解二阶锥约束变分不等式问题

刘雨 ¹ ,
孙菊贺 ¹ ,
王莉 ¹ ,
米娜 ¹ ,
袁艳红 ²

作者信息 +

An augmented Lagrange method for solving second-order cone-constrained variational inequalities

Yu LIU ¹ ,
Juhe SUN ¹ ,
Li WANG ¹ ,
Na MI ¹ ,
Yanhong YUAN ²

Author information +

文章历史 +

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摘要

应用增广Lagrange方法求解了一类二阶锥约束变分不等式问题。首先，将二阶锥约束变分不等式问题转化为等价的优化问题，从而得到其不同的等价形式；其次，应用投影算子的性质，将二阶锥约束变分不等式问题转化为方程组问题，并针对方程组问题提出了增广Lagrange方法；再次，讨论了算法的全局收敛性，同时对算法的一个特殊情况进行了深入分析，并引入一类非精确牛顿法求解算法中蕴含的子问题；最后，给出3个算例的数值实验结果，验证了算法的可行性。

Abstract

The augmented Lagrange method was applied to solve a class of cone-constrained variational inequalities of second-order. Firstly， the second-order cone-constrained variational inequality problem was transformed into an equivalent optimization problem， and its different equivalent forms were obtained. Secondly， the second-order cone-constrained variational inequality problem was transformed into a system of equations by using the properties of projection operator， and the augmented Lagrange method was proposed for the system of equations. Thirdly， the global convergence of the algorithm was discussed， and a special case of the algorithm was deeply analyzed， and a class of inexact Newton method was introduced to solve the subproblems contained in the algorithm. Finally， three numerical examples were given to verify the feasibility of the algorithm.