Lack of Equality between Abel and Cesaro Limits in Discrete Optimal Control and the Implied Duality Gap

In the recent paper [4] it has been shown that if Cesàro and Abel limits for a certain discrete time optimal control problem are not equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper, we construct an example of a problem satisfying the assumptions of [4] where Cesàro and Abel limits are different

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Work Title Lack of Equality between Abel and Cesaro Limits in Discrete Optimal Control and the Implied Duality Gap
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Open Access
Creators
  1. Ilya Shvartsman
Keyword
  1. optimal control
  2. discrete systems
  3. infinite horizon
  4. long-run average
  5. discounting
  6. Abel and Cesaro limits
  7. Tauberian theorem
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Pure and Applied Functional Analysis
Publication Date December 2021
Deposited August 16, 2024

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Version 1
published

  • Created
  • Added PAFA_revised_2.pdf
  • Added Creator Ilya Shvartsman
  • Published
  • Updated
  • Updated Keyword Show Changes
    Keyword
    • optimal control, discrete systems, infinite horizon, long-run average, discounting, Abel and Cesaro limits, Tauberian theorem
  • Updated Description Show Changes
    Description
    • In the recent paper [4] it has been shown that if Ces`aro and Abel limits for a certain discrete time optimal control problem are not
    • equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper, we construct an example of a problem satisfying the assumptions of [4] where Ces`aro and Abel limits are different
    • In the recent paper [4] it has been shown that if Cesaro and Abel limits for a certain discrete time optimal control problem are not
    • equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper, we construct an example of a problem satisfying the assumptions of [4] where Cesaro and Abel limits are different
  • Updated Description Show Changes
    Description
    • In the recent paper [4] it has been shown that if Cesaro and Abel limits for a certain discrete time optimal control problem are not
    • equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper, we construct an example of a problem satisfying the assumptions of [4] where Cesaro and Abel limits are different
    • In the recent paper [4] it has been shown that if Cesàro and Abel limits for a certain discrete time optimal control problem are not
    • equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper, we construct an example of a problem satisfying the assumptions of [4] where Cesàro and Abel limits are different
  • Updated Publication Date Show Changes
    Publication Date
    • 2021-12-01
    • 2021-12