Distributed Computational Framework for Large-Scale Stochastic Convex Optimization

Vahab Rostampour and Tamás Keviczky
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Vahab Rostampour: Engineering and Technology Institute Groningen (ENTEG), University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
Tamás Keviczky: Delft Center for Systems and Control, Delft University of Technology, 2628 CD Delft, The Netherlands

Energies, 2020, vol. 14, issue 1, 1-26

Abstract: This paper presents a distributed computational framework for stochastic convex optimization problems using the so-called scenario approach. Such a problem arises, for example, in a large-scale network of interconnected linear systems with local and common uncertainties. Due to the large number of required scenarios to approximate the stochasticity of these problems, the stochastic optimization involves formulating a large-scale scenario program, which is in general computationally demanding. We present two novel ideas in this paper to address this issue. We first develop a technique to decompose the large-scale scenario program into distributed scenario programs that exchange a certain number of scenarios with each other to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the decomposition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both local and common uncertainty sources. As our second contribution, we develop a so-called soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between the subproblems. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. Two different simulation studies of two types of interconnected network, namely dynamically coupled and coupling constraints, are presented to illustrate advantages of the proposed distributed framework.

Keywords: stochastic optimization; scenario convex program; distributed computation; distributed stochastic systems; distributed scenario program; decentralized scenario program; plug-and-play framework (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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