A policy iteration algorithm for fixed point problems with nonexpansive operators

@article{Chancelier2007API,
  title={A policy iteration algorithm for fixed point problems with nonexpansive operators},
  author={Jean-Philippe Chancelier and Marouen Messaoud and Agn{\`e}s Sulem},
  journal={Math. Meth. of OR},
  year={2007},
  volume={65},
  pages={239-259}
}
The aim of this paper is to solve the fixed point problems : v = Ov, with Ov(x) def = max(Lv(x), Bv(x)), x ∈ E , (1) where E is a finite set, L is contractive and B is a nonexpansive operator and v = Ov, with Ov(x) def = max(sup w Lv(x), sup z Bv(x)), x ∈ E , (2) where W and Z are general control sets, the operators L are contractive and operators B are nonexpansive. For these two problems, we give conditions which imply existence and uniqueness of a solution and provide a policy iteration… CONTINUE READING
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