Extremal problems for discrete and differential inclusions of hyperbolic type with distributed parameters

1990 ◽  
Vol 42 (12) ◽  
pp. 1476-1483 ◽  
Author(s):  
�. N. Makhmudov
Keyword(s):  
Differential Inclusions ◽  
Extremal Problems ◽  
Hyperbolic Type ◽  
Distributed Parameters

scholarly journals ON THE EXACT PENALTY OF HIGH ORDER FOR EXTREME PROBLEMS OF DIFFERENTIAL INCLUSIONS

2021 ◽  
Vol 6 (2(52)) ◽  
pp. 75-86
Author(s):  
Misraddin Allahverdi oglu Sadygov
Keyword(s):  
Distance Function ◽  
Differential Inclusions ◽  
Continuous Functions ◽  
Extremal Problems ◽  
High Order ◽  
Necessary Condition ◽  
Exact Penalty ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Locally Lipschitz

In this paper, using theorems on the continuous dependence of the solution of differential inclusions on the perturbation, we obtain high-order exact penalty theorems for nonconvex extremal problems of differential inclusions in the space of Banach-valued absolutely continuous functions. Using the type of the distance function in the classes of 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz functions, the nonconvex extremal problem for differential inclusions is reduced to a variational problem and the necessary condition for the extremum of a high-order is obtained. The paper also shows that the used functions type of distance function satisfy the 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz conditions.

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