Consistent mean field optimality conditions for interacting agent systems

Michael Herty, Christian Ringhofer

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We are interested in the derivation of optimality conditions for controlled interacting agent systems. We establish the relation between mean field optimality conditions and the optimality condition of the mean field control problem. This link is important for many recently published articles on control strategies for agent based systems since it establishes the precise relation between multipliers for the individual agents and the probability density distribution of the multipliers in the mean field limit. The relation to different notions of differentiability are also shown.

Original languageEnglish (US)
Pages (from-to)1095-1108
Number of pages14
JournalCommunications in Mathematical Sciences
Issue number4
StatePublished - 2019


  • Kinetic equations
  • Meanfield limits
  • Optimal control
  • Particle systems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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