Optimal Control of Random Sequences in Problems with Constraints

Piunovskiy, Alexey

doi:10.1007/978-94-011-5508-3

Cited by 109 publications

(107 citation statements)

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“…is continuous and bounded if the function f (x, a) is countinuous and bounded [5].) Therefore theorems from Section 3 imply the following properties of the space D od (the more detailed reasonings can be found in [5]):…”

Section: Definitionmentioning

confidence: 99%

“…The constructions presented are traditional for the theory of controlled stochastic sequences [1]- [5].…”

Section: Remarkmentioning

confidence: 99%

“…Therefore theorems from Section 3 imply the following properties of the space D od (the more detailed reasonings can be found in [5]):…”

Section: Definitionmentioning

confidence: 99%

“…The dot and dash straight line is the level curve S(P π ) = 0, that is The particular example λ(a) = √ a was considered in [5] (the version of the average losses).…”

Section: Example: Optimization Of Publicity Expensesmentioning

confidence: 99%

“…The advantage of such approach is the possibility of the investigation of control problems under functional constraints and other problems of vector optimization. The convex programming approach is presented in [4] for models with the denumerable state space and in [5] for general Borel models; the similar approach is used also in [6,7], see also other works of the same authors. The first stage of such investigation is the study of the strategic measures space.…”

Section: Introductionmentioning

confidence: 99%

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Strategic measures in optimal control problems for stochastic sequences

Mao

Piunovskiy

2000

Stochastic Analysis and Applications

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Section: Definitionmentioning

confidence: 99%

“…The constructions presented are traditional for the theory of controlled stochastic sequences [1]- [5].…”

Section: Remarkmentioning

confidence: 99%

“…Therefore theorems from Section 3 imply the following properties of the space D od (the more detailed reasonings can be found in [5]):…”

Section: Definitionmentioning

confidence: 99%

“…The dot and dash straight line is the level curve S(P π ) = 0, that is The particular example λ(a) = √ a was considered in [5] (the version of the average losses).…”

Section: Example: Optimization Of Publicity Expensesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strategic measures in optimal control problems for stochastic sequences

Mao

Piunovskiy

2000

Stochastic Analysis and Applications

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Multiple Objective Nonatomic Markov Decision Processes with Total Reward Criteria

Feinberg

Piunovskiy

2000

Journal of Mathematical Analysis and Applications

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We consider a Markov decision process with an uncountable state space and multiple rewards. For each policy, its performance is evaluated by a vector of total expected rewards. Under the standard continuity assumptions and the additional assumption that all initial and transition probabilities are nonatomic, we prove that the set of performance vectors for all policies is equal to the set of performance Ž . vectors for nonrandomized Markov policies. This result implies the existence of Ž . optimal nonrandomized Markov policies for nonatomic constrained Markov decision processes with total rewards. We provide two examples of applications of our results to constrained multiple objective problems in inventory control and finance.

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