LP formulations of discrete time long-run average optimal control problems

the nonergodic case

Vivek S. Borkar, Vladimir Gaitsgory, Ilya Shvartsman

Research output: Contribution to journalArticle

1 Citation (Scopus)


We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to characterize the optimal value of the optimal control problem. The novelty of our approach is that we focus on the general case wherein the optimal value may depend on the initial condition of the system.

Original languageEnglish
Pages (from-to)1783-1817
Number of pages35
JournalSIAM Journal on Control and Optimization
Issue number3
Publication statusPublished - 21 May 2019


  • Duality
  • Infinite horizon and vanishing discount limits
  • Linear programming
  • Long-run average optimal control
  • Sufficient/necessary optimality conditions

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