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

Dario Bauso, Quanyan Zhu, Tamer Başar

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)606-630
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume169
Issue number2
DOIs
StatePublished - May 1 2016

Keywords

  • Mean-field games
  • Mixed integer optimization
  • Optimal control

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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