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

Author

Listed:
  • Dario Bauso

    (The University of Sheffield
    Università di Palermo)

  • Quanyan Zhu

    (Polytechnic School of Engineering New York University)

  • Tamer Başar

    (University of Illinois at Urbana-Champaign)

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.

Suggested Citation

  • Dario Bauso & Quanyan Zhu & Tamer Başar, 2016. "Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 606-630, May.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-016-0881-6
    DOI: 10.1007/s10957-016-0881-6
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    References listed on IDEAS

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    Cited by:

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