Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems

Dario Bauso*, Quanyan Zhu, Tamer Basar

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review

1 Citaat (Scopus)
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Samenvatting

Mixed integer optimal compensation deals with optimization problems with integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of an exogenous signal and the local state average. We discuss a large population mean-field type of approximation and extend our study to opinion dynamics in social networks as a special case of interest.

Originele taal-2English
Pagina's (van-tot)606-630
Aantal pagina's25
TijdschriftJournal of optimization theory and applications
Volume169
Nummer van het tijdschrift2
DOI's
StatusPublished - mei-2016
Extern gepubliceerdJa

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