Online Proximal-ADMM for Time-Varying Constrained Convex Optimization

This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly possibly non-differentiable, variables are coupled through linear constraints. In this setting, the proposes an online algorithm based on alternating direction method of multipliers (ADMM), track optimal solution trajectory time-varying problem; in particular, proposed consists primal proximal gradient descent step appropriately perturbed dual ascent step. derives tracking results, asymptotic bounds, convergence results.The then specialized multi-area power grid problem, our numerical results verify desired properties.