论文标题
在线近端ADMM，用于时变约束的凸优化
Online Proximal-ADMM For Time-varying Constrained Convex Optimization
论文作者
论文摘要
本文考虑了凸优化问题，其成本和限制随着时间的流逝而发展。要最小化的函数强烈凸出，并且可能是非差异的，并且变量通过线性约束耦合。在这种情况下，本文提出了一种基于乘数的交替方向方法（ADMM）的在线算法，以跟踪时变问题的最佳解决方案轨迹；特别是，提出的算法包括一个原始的近端梯度下降步骤和适当的双重上升步骤。该论文得出跟踪结果，渐近边界和线性收敛结果。然后，所提出的算法专门针对多面积功率电网优化问题，我们的数值结果验证了所需的属性。
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In this setting, the paper proposes an online algorithm based on the alternating direction method of multipliers (ADMM), to track the optimal solution trajectory of the time-varying problem; in particular, the proposed algorithm consists of a primal proximal gradient descent step and an appropriately perturbed dual ascent step. The paper derives tracking results, asymptotic bounds, and linear convergence results. The proposed algorithm is then specialized to a multi-area power grid optimization problem, and our numerical results verify the desired properties.
