On Duality in Second-Order Discrete and Differential Inclusions with Delay

Mahmudov, Elimhan N.

doi:10.1007/s10883-019-09471-4

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Besides, many of the necessary and sufficient conditions for optimization of differential inclusions inevitably require the creation of new types of equivalence in the Mahmudov survey papers [20]- [26]. The paper [28] develops the theory of duality for the Mayer problem given by second-order evolution differential inclusions with delay and state constraints. Although all the proofs in that work relating to dual problems are carried out in the case of delay, the results are also considered without delay.…”

Section: Introductionmentioning

confidence: 99%

Polyhedral optimization of second-order discrete and differential inclusions with delay

Sağlam¹,

Mahmudov²

2021

Turk J Math

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The present paper studies the optimal control theory of second-order polyhedral delay discrete and delaydifferential inclusions with state constraints. We formulate the conditions of optimality for the problems with the secondorder polyhedral delay-discrete (P D d) and the delay-differential (P C d) in terms of the Euler-Lagrange inclusions and the distinctive "transversality" conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.

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Section: Introductionmentioning

confidence: 99%

Polyhedral optimization of second-order discrete and differential inclusions with delay

Sağlam¹,

Mahmudov²

2021

Turk J Math

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“…Essentially, the optimal control problems with ordinary and partial differential inclusions consist of intensive areas of development in the applied mathematical theory of analysis. Note that the reader can consult on the various problems described in the multi-valued mappings [15]- [27], [29], [? ], [37].…”

Section: Introductionmentioning

confidence: 99%

Optimality conditions for higher order polyhedral discrete and differential inclusions

Sağlam

Mahmudov

2020

Filomat

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The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.

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Duality in optimal control with first order partial differential inclusions

Mahmudov

2021

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On Duality in Second-Order Discrete and Differential Inclusions with Delay

Cited by 3 publications

References 28 publications

Polyhedral optimization of second-order discrete and differential inclusions with delay

Polyhedral optimization of second-order discrete and differential inclusions with delay

Optimality conditions for higher order polyhedral discrete and differential inclusions

Duality in optimal control with first order partial differential inclusions

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