Linear Programming Formulation of Long-Run Average Optimal Control Problem

  • Vivek S. Borkar
  • Vladimir GaitsgoryEmail author


We formulate and study the infinite-dimensional linear programming problem associated with the deterministic long-run average cost control problem. Along with its dual, it allows one to characterize the optimal value of this 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.


Long-run average optimal control Linear programming Duality Infinite horizon Vanishing discount limits 

Mathematics Subject Classification

34E15 34C29 93C70 



The work on this paper was initiated, while V.S. Borkar was visiting the Department of Mathematics at Macquarie University. The research was supported in part by a J. C. Bose Fellowship from the Government of India and in part by the Australian Research Council Discovery Grant DP150100618.


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Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology BombayPowai, MumbaiIndia
  2. 2.Department of Mathematics and StatisticsMacquarie UniversitySydneyAustralia

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