Optimal control of higher order viable differential inclusions and duality

Mahmudov, Elimhan N.

doi:10.1080/00036811.2020.1813725

Cited by 6 publications

(2 citation statements)

References 22 publications

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“…Here, adjoint differential inclusion is constructed using the discrete method of the continuous problem. It is noteworthy that condition (i) of Theorem 3.1 is immediately deduced from the adjoint Mahmudov's differential inclusions [19].…”

Section: Optimality Conditions Of Periodic Boundary Problemmentioning

confidence: 96%

“…In contrast to the Lagrange and Fenchel duality, Mahmudov successfully constructed the duality for problems with differential inclusions using the concept of dual operations of addition and infimal convolution of convex functions. The difficulties that have arisen in this case are related to the fact that this approach necessarily requires the construction of a duality of coupled discrete and discrete approximate problems [9,10,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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On duality in convex optimization of second-order differential inclusions with periodic boundary conditions

Sağlam

Mahmudov

2022

Hacettepe Journal of Mathematics and Statistics

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The present paper is devoted to the duality theory for the convex optimal control problem of second-order differential inclusions with periodic boundary conditions. First, we use an auxiliary problem with second-order discrete-approximate inclusions and focus on formulating sufficient conditions of optimality for the differential problem. Then, we concentrate on the duality that exists in periodic boundary conditions to establish a dual problem for the differential problem and prove that Euler-Lagrange inclusions are duality relations for both primal and dual problems. Finally, we consider an example of the duality for the second-order linear optimal control problem.

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Section: Optimality Conditions Of Periodic Boundary Problemmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%