Approximate solutions of the bellman equation of deterministic control theory

I. Capuzzo Dolcetta*, H. Ishii

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

109 Citations (Scopus)


We consider an infinite horizon discounted optimal control problem and its time discretized approximation, and study the rate of convergence of the approximate solutions to the value function of the original problem. In particular we prove the rate is of order 1 as the discretization step tends to zero, provided a semiconcavity assumption is satisfied. We also characterize the limit of the optimal controls for the approximate problems within the framework of the theory of relaxed controls.

Original languageEnglish
Pages (from-to)161-181
Number of pages21
JournalApplied Mathematics & Optimization
Issue number1
Publication statusPublished - 1984 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)


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