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The Expected Total Cost Criterion

  • Onésimo Hernández-Lerma
  • Jean Bernard Lasserre
Chapter
Part of the Applications of Mathematics book series (SMAP, volume 42)

Abstract

Let \( M = (X,A,\{ A(x)\left| x \right. \in X\} ,Q,c) \) be the Markov control model (MCM) in §8.2. In this chapter we study the expected total cost (ETC) criterion defined as
$$ {V_1}(\pi ,x): = E_x^\pi \left[ {\sum\limits_{t = 0}^\infty {c({x_t} - {a_t})} } \right] for \pi \in \Pi ,x \in X, $$
(9.1.1)
so the corresponding (optimal) value function is
$$ V_1^*(x): = \mathop {\inf }\limits_\Pi {V_1}(\pi ,x), x \in X. $$
(9.1.2)

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Onésimo Hernández-Lerma
    • 1
  • Jean Bernard Lasserre
    • 2
  1. 1.Departamento de MatemáticasCINVESTAV-IPNMexico DFMexico
  2. 2.LAAS-CNRSToulouse CedexFrance

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