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)1-25
Number of pages25
JournalJournal of Optimization Theory and Applications
DOIs
StateAccepted/In press - Feb 17 2016

Fingerprint

Mean Field
Decomposition
Decompose
Integer
Integer programming
Multi agent systems
Linear programming
Dynamical systems
Decomposition Method
Scalar
Opinion Dynamics
Optimization Problem
Zero sum game
Lot Sizing
Mixed Integer Programming
Shortest path
Coupled System
Social Networks
Multi-agent Systems
Dynamic Systems

Keywords

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

ASJC Scopus subject areas

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

Cite this

Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems. / Bauso, Dario; Zhu, Quanyan; Başar, Tamer.

In: Journal of Optimization Theory and Applications, 17.02.2016, p. 1-25.

Research output: Contribution to journalArticle

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