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| 摘要: |
| 本文研究了大规模的可分离带线性约束的变分不等式问题，提出了基于对数二次临近点法的交替方向法，新算法的每步用一个非线性方程组来代替变分不等式子问题.通过有效求解非线性方程组，使得新算法简单易行而且一定程度上提高了计算的效率.同时，在映射单调和原问题解集非空的条件下，证明了此算法具有全局收敛性，最后通过数值实验说明了此算法是有效可行的. |
| 关键词: 变分不等式 交替方向法 全局收敛性 |
| DOI： |
| 分类号:O177.91 |
| 基金项目:江苏省高校自然科学研究面上项目（16KJB110009）；江苏省自然科学基金（BK20171041）；江苏高校哲学社会科学研究项目（2017SJB0238）. |
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| A MIXED ALGORITHM FOR SOLVING SEPARABLE VARIATIONAL INEQUALITIES WITH LINEAR CONSTRAINTS |
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ZHANG Cong-jun,LI Sai,LÜ Li-xia,WANG Yue-hu
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| Abstract: |
| In this paper, we study large-scale separable variational inequality problem with linear constraints. Also, we propose a new alternating direction method which is based on the logarithmic-quadratic proximal method. By this method, we have nonlinear equations instead of sub-variational inequalities and it solves structural variational inequalities quickly. Meanwhile, mappings are monotonous and the solution set of the original problem is non-empty, we prove the new algorithm's global convergence, and the algorithm is effective and feasible. |
| Key words: variational inequality alternating direction method global convergence |
