Discrete-time interval optimal control problem

Campos, José Renato; Assunção, Edvaldo; Silva, Geraldo Nunes; Lodwick, Weldon A.; Teixeira, Marcelo Carvalho Minhoto

doi:10.1080/00207179.2017.1410575

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…In most research on modeling uncertainties in optimal control problems, the interval and fuzzy sets are conventional to show uncertainty. See [1,3,8,10,11,21,26]. Zhao and Zhu [26] studied an optimal control problem with a quadratic cost function based on fuzzy concepts.…”

Section: Introductionmentioning

confidence: 99%

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

2023

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In this paper, we study an optimal control problem in which their cost function is interval-valued. Also, a stochastic differential equation governs their state space. Moreover, we introduce a generalized version of Bellman's optimality principle for the stochastic system with an interval-valued cost function. Also, we obtain the Hamilton-Jacobi-Bellman equations and their control decisions. Two numerical examples happen in finance in which their cost function are interval-valued functions, illustrating the efficiency of the discussed results. The obtained results provide significantly reliable decisions compared to the case where the conventional cost function is applied.

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Section: Introductionmentioning

confidence: 99%

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

2023

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“…In this case, the CIA presents a smaller width interval, thus improving the overestimation of Moore's arithmetic [30]. Actually, CIA has been used to solve several mathematical problems, such as in [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Developing Constrained Interval Operators for Fuzzy Logic with Interval Values

Pinheiro,

Santiago,

Bedregal

et al. 2023

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A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is shown that a large part of the properties studied is preserved by this operator, while others remain preserved with the condition of continuity, as is the case of the exchange principle. In addition, a comparative study is carried out between this operator g¨ and the best interval representation: g^. Although g¨⊆g^ and g¨ do not preserve the Moore correction, we do not have a loss of relevant information since everything that is lost is irrelevant, mitigating the overestimation.

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“…In addition, the anticipation of the worst case over all possible scenarios is crucial in many practical applications (Aissi et al 2009). Therefore, the minimax regret criterion is applied in a broad spectrum of real-world domains, including finance, supply chain management, statistics, and engineering, to address issues including portfolio optimization (Xidonas et al 2017;Caçador et al 2020;Mohammadi and Mohammadi 2018;Li and Wang 2020;Giove et al 2006), inventory control (Yue et al 2006;Roels 2008, 2010;Ni et al 2019;Campos et al 2019), learning and estimation (Bartók et al 2014;Alaiz-RodrÃguez et al 2007;Eldar and Merhav 2004), behavior prediction (Jiang et al 2013;Hayashi 2008;Kazakçi et al 2007), and power control (Chen et al 2014;Jo and Joo 2015;Dong et al 2011;Li et al 2018). Among which a typical example is the relative robust portfolio proposed by Caçador et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Robust pricing for airlines with partial information

2021

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In the spot market for air cargo, airlines typically adopt dynamic pricing to tackle demand uncertainty, for which it is difficult to accurately estimate the distribution. This study addresses the problem where a dominant airline dynamically sets prices to sell its capacities within a two-phase sales period with only partial information. That partial information may show as the moments (upper and lower bounds and mean) and the median of the demand distribution. We model the problem of dynamic pricing as a distributional robust stochastic programming, which minimizes the expected regret value under the worst-case distribution in the presence of partial information. We further reformulate the proposed non-convex model to show that the closed-form formulae of the second-stage maximal expected regret are well-structured. We also design an efficient algorithm to characterize robust pricing strategies in a polynomial-sized running time. Using numerical analysis, we present several useful managerial insights for airline managers to strategically collect demand information and make prices for their capacities in different market situations. Moreover, we verify that additional information will not compromise the viability of the pricing strategies being implemented. Therefore, the method we present in this paper is easier for airlines to use.

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Discrete-time interval optimal control problem

Cited by 5 publications

References 13 publications

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function

Developing Constrained Interval Operators for Fuzzy Logic with Interval Values

Robust pricing for airlines with partial information

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