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**Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions.**
*(English)*
Zbl 1476.49029

Summary: The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying infimal convolution concept of convex functions, step by step we construct the dual problems for discrete, discrete-approximate and differential inclusions and prove duality results. It seems that the Euler-Lagrange type inclusions are “duality relations” for both primary and dual problems and that the dual problem for discrete-approximate problem make a bridge between them. At the end of the paper duality in problems with second order linear discrete and continuous models and model of control problem with polyhedral DFIs are considered.

### MSC:

49K15 | Optimality conditions for problems involving ordinary differential equations |

49J52 | Nonsmooth analysis |

49N15 | Duality theory (optimization) |

34A60 | Ordinary differential inclusions |

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\textit{E. N. Mahmudov}, Evol. Equ. Control Theory 10, No. 1, 37--59 (2021; Zbl 1476.49029)

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