On ε-optimal continuous selectors and their application in discounted dynamic programming

  • A. Kucia
  • A. Nowak
Contributed Papers
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Abstract

LetX,Y be topological spaces, ϕ:X→2 Y a multifunction, andu a real-valued function defined on the graph of ϕ. We give sufficient conditions for the existence of a continous selectorf for ϕ such that
$$u(x,f(x)) \geqslant \sup \{ u(x,y):y \in \varphi (x)\} - \varepsilon , x \in X,$$
where ε>0. This result is applied to the stochastic discounted dynamic programming problem. We establish the existence of an ε-optimal continuous stationary policy.

Key Words

Parametric optimization qualitative stability ε-optimal continuous selector discounted dynamic programming ε-optimal policy 

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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • A. Kucia
    • 1
  • A. Nowak
    • 1
  1. 1.Institute of MathematicsSilesian UniversityKatowicePoland

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