论文标题
将历史和偏差纳入前后分裂
Incorporating History and Deviations in Forward--Backward Splitting
论文作者
论文摘要
我们提出了一种求解结构化单调夹杂物的前向反向分裂方法的变体。我们的方法将过去的迭代和两个偏差向量集成到更新方程中。这些偏差向量为算法带来了灵活性，只要它们共同满足规范条件，就可以任意选择。我们提出特殊情况，其中选择为先前迭代的预定线性组合的偏差向量始终符合规范条件。值得注意的是，我们采用标量参数引入了一种算法，以在传统的前向反向分裂方案和加速的O（1/n^2）之间插值，并涵盖了加速前向前的方法，该方法涵盖了加速邻近点方法和Halpern迭代作为特殊情况。现有方法对应于允许的标量参数范围的两个极端。通过在允许范围的中点附近选择插值标量，我们的算法在解决最小值优化引起的基本单调包含问题时，显着优于这些先前已知的方法。
We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility to the algorithm and can be chosen arbitrarily as long as they together satisfy a norm condition. We present special cases where the deviation vectors, selected as predetermined linear combinations of previous iterates, always meet the norm condition. Notably, we introduce an algorithm employing a scalar parameter to interpolate between the conventional forward--backward splitting scheme and an accelerated O(1/n^2)-convergent forward--backward method that encompasses both the accelerated proximal point method and the Halpern iteration as special cases. The existing methods correspond to the two extremes of the allowed scalar parameter range. By choosing the interpolation scalar near the midpoint of the permissible range, our algorithm significantly outperforms these previously known methods when addressing a basic monotone inclusion problem stemming from minimax optimization.
