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

Dario Bauso (), Quanyan Zhu () and Tamer Başar ()
Additional contact information
Dario Bauso: The University of Sheffield
Quanyan Zhu: Polytechnic School of Engineering New York University
Tamer Başar: University of Illinois at Urbana-Champaign

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 2, No 13, 606-630

Abstract: 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.

Keywords: Mean-field games; Optimal control; Mixed integer optimization; 91A13; 49J35; 49L20; 90C11 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-0881-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-016-0881-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-0881-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().