LP-related representations of Cesàro and Abel limits of optimal value functions

We consider infinite horizon optimal control problems with time averaging and time discounting criteria and derive linear programming-related representations of Cesàro and Abel limits of their optimal values in the case when they depend on the initial conditions. We show that Cesàro and Abel limits are equal if they are continuous functions of the initial condition, strengthening previous results that require uniform convergence to ensure this equality. The obtained representations of the limits of value functions are used to derive optimality conditions for the long-run average optimal control problem.

This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 2021-08-09, available online: https://www.tandfonline.com/10.1080/02331934.2021.1964078.

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Work Title LP-related representations of Cesàro and Abel limits of optimal value functions
Access
Open Access
Creators
  1. Vladimir Gaitsgory
  2. Ilya Shvartsman
Keyword
  1. Optimal control
  2. Infinite horizon
  3. Cesàro and Abel limits
  4. Linear programming
  5. Optimality conditions
License CC BY-NC 4.0 (Attribution-NonCommercial)
Work Type Article
Publisher
  1. Optimization
Publication Date August 9, 2021
Publisher Identifier (DOI)
  1. https://doi.org/10.1080/02331934.2021.1964078
Deposited February 17, 2023

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Version 1
published

  • Created
  • Added nonsmooth_LRA_revised.pdf
  • Added Creator Vladimir Gaitsgory
  • Added Creator Ilya Shvartsman
  • Published
  • Updated Keyword, Publication Date Show Changes
    Keyword
    • Optimal control, Infinite horizon, Cesàro and Abel limits, Linear programming, Optimality conditions
    Publication Date
    • 2022-01-01
    • 2021-08-09
  • Updated