论文标题
线性约束强烈凸出问题的惩罚方法的收敛率
Convergence Rate of a Penalty Method for Strongly Convex Problems with Linear Constraints
论文作者
论文摘要
我们考虑一个优化问题，具有强烈的凸目标和线性不平等的约束。为了能够处理大量限制，我们提供了对问题的罚款重新重新制定。作为惩罚功能，我们使用单方面的Huber损失的版本。这些功能的平滑度属性使我们能够选择随时间变化的惩罚参数，以使带有速度尺寸减小的逐步尺寸的增量过程收敛到精确解决方案，并带有速率$ o（1/{\ sqrt k}）$。据我们所知，我们介绍了基于惩罚的梯度方法的收敛率的第一个结果，在该方法中，惩罚参数随时间而变化。
We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a version of the one-sided Huber losses. The smoothness properties of these functions allow us to choose time-varying penalty parameters in such a way that the incremental procedure with the diminishing step-size converges to the exact solution with the rate $O(1/{\sqrt k})$. To the best of our knowledge, we present the first result on the convergence rate for the penalty-based gradient method, in which the penalty parameters vary with time.
