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.

中文翻译：

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时变约束凸优化的在线近距ADMM

本文考虑了一个凸优化问题，该问题的成本和约束条件会随着时间而发展。要最小化的函数是强凸的，并且可能是不可微的，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交替方向法（ADMM）的在线算法，以跟踪时变问题的最优解轨迹。特别地，所提出的算法包括原始近端梯度下降步骤和适当扰动的双重上升步骤。本文导出了跟踪结果，渐近边界和线性收敛结果，然后将所提出的算法专门用于多区域电网优化问题，我们的数值结果验证了所需的特性。