In this paper we consider a distributed optimiza- tion scenario in which a set of processors aims at minimizing the maximum of a collection of “separable convex functions” subject to local constraints. This set-up is motivated by peak- demand minimization problems in smart grids. Here, the goal is to minimize the peak value over a finite horizon with: (i) the demand at each time instant being the sum of contributions from different devices, and (ii) the local states at different time instants being coupled through local dynamics. The min-max structure and the double coupling (through the devices and over the time horizon) makes this problem challenging in a distributed set-up (e.g., well-known distributed dual decompo- sition approaches cannot be applied). We propose a distributed algorithm based on the combination of duality methods and properties from min-max optimization. Specifically, we derive a series of equivalent problems by introducing ad-hoc slack variables and by going back and forth from primal and dual formulations. On the resulting problem we apply a dual sub- gradient method, which turns out to be a distributed algorithm. We prove the correctness of the proposed algorithm and show its effectiveness via numerical computations

A duality-based approach for distributed min-max optimization with application to demand side management

Notarnicola Ivano;Notarstefano Giuseppe
2016

Abstract

In this paper we consider a distributed optimiza- tion scenario in which a set of processors aims at minimizing the maximum of a collection of “separable convex functions” subject to local constraints. This set-up is motivated by peak- demand minimization problems in smart grids. Here, the goal is to minimize the peak value over a finite horizon with: (i) the demand at each time instant being the sum of contributions from different devices, and (ii) the local states at different time instants being coupled through local dynamics. The min-max structure and the double coupling (through the devices and over the time horizon) makes this problem challenging in a distributed set-up (e.g., well-known distributed dual decompo- sition approaches cannot be applied). We propose a distributed algorithm based on the combination of duality methods and properties from min-max optimization. Specifically, we derive a series of equivalent problems by introducing ad-hoc slack variables and by going back and forth from primal and dual formulations. On the resulting problem we apply a dual sub- gradient method, which turns out to be a distributed algorithm. We prove the correctness of the proposed algorithm and show its effectiveness via numerical computations
2016 IEEE 55th Conference on Decision and Control
1877
1882
Notarnicola Ivano; Franceschelli Mauro; Notarstefano Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/674752
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