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 language | English (US) |
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Pages (from-to) | 606-630 |
Number of pages | 25 |
Journal | Journal of Optimization Theory and Applications |
Volume | 169 |
Issue number | 2 |
DOIs | |
State | Published - 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