On necessary optimality conditions in discrete control systems

Mardanov, Mısır J.; Melikov, T. K.; Mahmudov, Nazım I.

doi:10.1080/00207179.2015.1035756

Cited by 13 publications

(15 citation statements)

References 20 publications

(21 reference statements)

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“…To sum up, this is the first paper to discuss the discrete-time forward-backward stochastic optimal control problems of mean-field type under weaker convexity assumption, enabling us to establish the more general and constructive SMP. Our work generalizes and enhances the previously known SMP of [19,23]. Meanwhile, it extends the classical results of [17,23] to the mean-field theory as well as forwardbackward system.…”

Section: Introductionsupporting

confidence: 84%

“…Based on these arguments, we could obtain the dual principle. It is worth mentioning that our paper differs from [19] in the following aspects. Firstly, our work is based on a weaker convexity assumption.…”

Section: Introductionmentioning

confidence: 87%

“…Xu et al [16] considered the solvability of fully coupled FBS Es, in which the BS E was given as the conditional expectation form and the coefficients in the backward equation were degenerate. Some representative works in this direction include [17][18][19][20]. Very recently, Ji and Liu [21] first discussed the SMP for FBS Es under the convex control domain, which made substantial progresses in discrete-time forward-backward systems.…”

Section: Introductionmentioning

confidence: 99%

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A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type

Song

Liu

2020

Adv Differ Equ

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In this paper, we consider the optimal control problem for fully coupled forward-backward stochastic difference equations of mean-field type under weak convexity assumption. By virtue of employing a suitable product rule and formulating a mean-field backward stochastic difference equation, we establish the stochastic maximum principle and also derive, under additional assumptions, that the stochastic maximum principle is also a sufficient condition. As an application, a Stackelberg game of mean-field backward stochastic difference equation is presented to demonstrate our results.

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Section: Introductionsupporting

confidence: 84%

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type

Song

Liu

2020

Adv Differ Equ

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“…Moreover, it serves to generalize and extend the existing necessary conditions from previous works 21,29,30 . Additionally, it significantly enhances and expands upon the classical findings of earlier studies 31,32 by applying them to the mean‐field model.…”

Section: Introductionmentioning

confidence: 57%

Stochastic maximum principle for discrete time mean‐field optimal control problems

Ahmadova

Mahmudov

2023

Optim Control Appl Methods

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This article studies optimal control of a discrete‐time stochastic differential equation of mean‐field type with coefficients dependent on function of the law and state of the process. A new version of the maximum principle for discrete‐time mean‐field type stochastic optimal control problems is established, using new discrete‐time mean‐field backward stochastic equations. The cost functional is also of mean‐field type. The study derives necessary first‐order and sufficient optimality conditions using adjoint equations that take the form of discrete‐time backward stochastic differential equations with a mean‐field component. An optimization problem for production and consumption choice is used as an example.

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“…We particularly refer reader to works of E.N.Mahmudov for a thoroughly study of necessary and sufficient conditions for the optimality of the higher order differential inclusions of Bolza and Mayer types [12,16,[18][19][20]22]. [25][26][27] study high-order necessary optimality conditions for discrete optimal control problems. Second-order necessary optimality conditions for an optimal control problem with a non-convex cost function and state-control constraints are obtained in [31].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Mayer functional in problems with discrete and differential inclusions and viability constraints

ÇİÇEK,

MAHMUDOV

2021

Turk J Math

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This paper derives the optimality conditions for a Mayer problem with discrete and differential inclusions with viable constraints. Applying necessary and sufficient conditions of problems with geometric constraints, we prove optimality conditions for second order discrete inclusions. Using Locally Adjoint Mapping we derive Euler-Lagrange form conditions and transversality conditions for the optimality of the discrete approximation problem. Passing to the limit we establish sufficient conditions to the optimal problem with viable constraints. Conditions ensuring the existence of solutions to the viability problems for differential inclusions of second order have been studied in recent years. However, optimization problems of second-order differential inclusions with viable constraints considered in this paper have not been examined yet. The results presented here are motivated by practices for optimization of various fields as the mass movement model well known in traffic balance and operations research.

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On necessary optimality conditions in discrete control systems

Cited by 13 publications

References 20 publications

A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type

A maximum principle for fully coupled controlled forward–backward stochastic difference systems of mean-field type

Stochastic maximum principle for discrete time mean‐field optimal control problems

Optimization of Mayer functional in problems with discrete and differential inclusions and viability constraints

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