Optimal Control with Partially Observed Regime Switching: Discounted and Average Payoffs

Escobedo-Trujillo, Beatris Adriana; Garrido, Javier; Alcalá, Gerardo; Revuelta-Acosta, Josept David

doi:10.3390/math10122073

Cited by 2 publications

(1 citation statement)

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“…Recently, there has been a strong orientation of researchers towards the development of specific methods dedicated to certain processes in particular fields. The paper by [14] is centered on an optimal control problem with applications in car suspension systems and the accumulation of pollution caused by the consumption of gas, oil, etc. Shao et al [15] present a study of deregulated electricity using fuzzy variables and robust optimization so that the expectation of a risk-averse distribution system operator is fulfilled.…”

Section: Introductionmentioning

confidence: 99%

On Solving Stochastic Optimization Problems

Blăjină,

Ghionea

2023

Mathematics

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Many optimization mathematical models, associated with the technical-economic processes of real-world problems, have elements of uncertainty in their structure, which places them in stochastic optimization programming. Their diversity and complexity, due to the large uncertainty space, require special methods of solving, because there is no general solution method. Within this context, in this paper we consider the category of optimization models that can contain random variable type coefficients and/or imposed probability levels on the constraints. The purpose of the paper is to propose a methodology dedicated to these studied models. Applying the methodology leads to developing a deterministic linear programming model, associated with the initial stochastic model. In fact, the proposed methodology reduces the stochastic formulation to a deterministic formulation. The methodology is illustrated with a numerical case study based on a manufacturing problem. Solving the obtained deterministic model is carried out in the version assisted by a specialized software product (WinQSB Version 2.0). It allows for the performing of a sensitivity analysis of the optimal solution, and/or a parametric analysis relative to certain model coefficients, both also presented in the paper. The main result of the study in this paper is the proposed methodology, which is applicable on a large scale, for any mathematical model of stochastic optimization of the mentioned type, regardless of complexity, dimensions and the domain of the process to which it is associated. The numerical results obtained when applying this methodology indicate its efficiency and effectiveness in finding the solution for the studied models. The approach to this issue in the present paper is determined by the wide range of stochastic optimization problems in the various studied real-life processes and by the imperative need to adopt the best decisions in conditions of uncertainty.

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Section: Introductionmentioning

confidence: 99%