In this paper, by combining the logarithmic-quadratic proximal (LQP) method and alternating direction method, we proposed an LQP alternating direction method for solving structured variational inequalities. The new iterate is generated by searching the optimal step size along a descent direction with a new step size α_k. The choice of the descent direction and the step size selection strategies are important for the algorithm’s efficiency. The O(1/t) convergence rate of the proposed method is studied, and its efficiency is also verified by some numerical experiments.

中文翻译：

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结构变分不等式的自适应下降LQP交变方向方法

本文结合对数二次方近邻法和交变方向法，提出了一种求解结构变分不等式的LQP交变方向方法。新的迭代通过沿着与新的步长的下降方向搜索的最佳步长而生成α _ķ。下降方向的选择和步长选择策略对算法的效率很重要。研究了该方法的O（1 / t）收敛速度，并通过一些数值实验验证了其有效性。