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.

Bauso, D., Zhu, Q., Basar, T. (2016). Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 169, 606-630 [10.1007/s10957-016-0881-6].

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

D. Bauso;
2016-01-01

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.
2016
Settore MAT/09 - Ricerca Operativa
Settore ING-INF/04 - Automatica
Bauso, D., Zhu, Q., Basar, T. (2016). Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 169, 606-630 [10.1007/s10957-016-0881-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/253204
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