Mean field social optimization: feedback person-by-person optimality and the master equation
| Autor: | Minyi Huang, Li-Hsien Sun, Shuenn-Jyi Sheu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Optimization problem Computer science MathematicsofComputing_NUMERICALANALYSIS 02 engineering and technology Optimal control 01 natural sciences 010101 applied mathematics Dynamic programming Nonlinear system 020901 industrial engineering & automation Mean field theory ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Master equation Process control 0101 mathematics Probability measure |
| Zdroj: | CDC |
| DOI: | 10.1109/cdc42340.2020.9303898 |
| Popis: | This paper considers a nonlinear mean field social optimization problem which aims to minimize a social cost. By use of a finite player model, we apply dynamic programming to formalize a person-by-person (PbP) optimality condition in a feedback form. This procedure leads to a new Hamilton-Jacobi-Bellman equation which involves differentiation with respect to probability measure and is called the master equation of social optimization. For the linear-quadratic (LQ) case, an explicit solution of the master equation is obtained. |
| Databáze: | OpenAIRE |
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