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| 摘要: |
| 交替方向法作为一个经典算法，主要用于求解大规模的可分离带线性约束的变分不等式问题. 它将原变分不等式问题拆分成一系列子变分不等式问题来求解，同时大大降低了原问题的维数，但是分解得到的子变分不等式往往不易求解. 鉴于对数二次临近点法可以快速求解结构型变分不等式的优点，本文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，我们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 对数二次临近点法 交替方向法 全局收敛性 |
| DOI： |
| 分类号:O177.91 |
| 基金项目: |
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| A mixed algorthm for solving separable variational inequalities |
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Zhang congjun,lisai
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| Abstract: |
| As a classical algorithm, alternating direction method mainly used to solve large-scale separable variational inequality problem with linear constraints. It can split the original variational inequality into a series of lower-dimensional sub-ones, but the sub-variational inequalities are often difficult to solve. Considering that the logarithmic-quadratic proximal method can solve structural variational inequalities quickly, in this paper, we propose a new alternating direction method which is based on the logarithmic-quadratic proximal method. In this method, we have nonlinear equations instead of sub-variational inequalities. Then, in condition that mappings are monotonous and the solution set of the original problem is non-empty, we prove the new algorithm’s global convergence. And in numerical experiment, we verify the algorithm is effective and feasible. |
| Key words: variational inequality alternating direction method logarithmic |
