VISCOSITY SOLUTIONS FOR MCKEAN-VLASOV CONTROL ON A TORUS

H. Mete Soner, Qinxin Yan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

An optimal control problem in the space of probability measures and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a smooth Fourier-Wasserstein metric. A comparison result between the Lipschitz viscosity sub- and supersolutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.

Original languageEnglish (US)
Pages (from-to)903-923
Number of pages21
JournalSIAM Journal on Control and Optimization
Volume62
Issue number2
DOIs
StatePublished - 2024

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • McKean-Vlasov
  • Wasserstein metric
  • mean-field games
  • viscosity solutions

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