Double smoothing for time-varying distributed multiuser optimization

Abstract

Abstract-Constrained optimization problems that couple different cooperating users sharing the same communication network are often referred to as multiuser optimization programs. We are interested in convex discrete-time time-varying multiuser optimization, where the problem to be solved changes at each time step. We study a distributed algorithm to generate a sequence of approximate optimizers of these problems. The algorithm requires only one round of communication among neighboring users between subsequent time steps and, under mild assumptions, converges linearly to a bounded error floor whose size is dependent on the variability of the optimization problem in time. To develop the algorithm we employ a double regularization both in the primal and in the dual space. This increases the convergence rate and helps us in the convergence proof. Numerical results support the theoretical findings.

Online Stochastic Optimization of Networked Distributed Energy Resources

“…This is a standard assumption in the domain of time-varying optimization [34], [46] to characterize the variability of optimal solutions from the current timeslot to the next (and, hence, the variability of problem inputs). Letŷ t :" rŷ tJ ,ŷ t`1J , .…”

An Incentive-Based Online Optimization Framework for Distribution Grids

“…where φ > 0 is a predefined parameter (see e.g., [7], [32]). With the regularization term − φ 2 µ 2 , the resultant function L φ (z, µ) is strongly concave in the dual variables.…”

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Online Primal-Dual Methods With Measurement Feedback for Time-Varying Convex Optimization

“…(5)]. With respect to the time-varying problem formulations in [26]- [28], the paper provides results in the case of feedback-based methods. It is also worth pointing out that the proposed methodology can be cast within the domain of -gradient methods [29]- [31]; in this case, the paper extends the analysis of -gradient methods to time-varying settings.…”