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For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge’s theorem states lower… (More)

This note generalizes Berge’s maximum theorem to noncompact image sets. It also clarifies the results from E.A. Feinberg, P.O. Kasyanov, N.V. Zadoianchuk, “Berge’s theorem for noncompact image sets,”… (More)

- Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
- Math. Oper. Res.
- 2016

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has… (More)

- Eugene A. Feinberg, Pavlo O. Kasyanov, Nina V. Zadoianchuk
- Math. Oper. Res.
- 2012

This paper presents sufficient conditions for the existence of stationary optimal policies for average cost Markov decision processes with Borel state and action sets and weakly continuous transition… (More)

S f(s)μ(ds) = 1, ∫ S f(s)μn(ds) = 0, and (1.3) does not hold. Theorem 1.1 presents Fatou’s lemma for weakly converging measures μn and nonnegative functions fn. This fact is useful for the analysis… (More)

and Applied Analysis 3 an evolution triple V ⊂ H ⊂ V ∗ see, e.g., 8 with dense and compact embeddings. We denote by 〈·, ·〉V the duality of V and its dual V ∗, by ‖ · ‖V ∗ the norm in V ∗. We have 〈u,… (More)

- Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
- 2014 IEEE Symposium on Adaptive Dynamic…
- 2014

This paper describes conditions for convergence to optimal values of the dynamic programming algorithm applied to total-cost Markov Decision Processes (MDPSs) with Borel state and action sets and… (More)

This paper compares and generalizes Berge’s maximum theorem for noncompact image sets established in Feinberg, Kasyanov and Voorneveld [5] and the local maximum theorem established in Bonnans and… (More)

- Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
- 52nd IEEE Conference on Decision and Control
- 2013

This note describes sufficient conditions for the existence of optimal policies for Partially Observable Markov Decision Processes (POMDPs). The objective criterion is either minimization of total… (More)

This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise convergence, and convergence in total variation. First, it describes and… (More)