一种解可分凸优化问题的外梯度并行分裂算法

摘要

Parallel splitting method is an important method for solving the convex optimization problem with two separable variables.The methods usually requires that the two convex functions have relatively easy proximal mappings,for the structure that only one of the two functions has easy proximal mapping and the other one is smoothly convex but does not have an easy proximal mapping.We propose in this paper an extragradient algorithm based on parallel splitting.Under the assumption that the smooth function has a Lipschitz continuous gradient condition,we prove the O(1/ε)iteration complexity of the method.%并行分裂法是求解两个可分离变量线性约束凸优化问题的重要方法，该方法通常要求两个凸函数有邻近映射，对于其中一个函数具有邻近映射，另一个函数光滑但不具有邻近映射的情况，此处提出了一种基于并行分裂的外梯度算法，并在假设光滑函数梯度Lipschitz连续条件下证明了该算法的O（1／ε）迭代复杂度。