Open AccessON THE EXACT PENALTY OF HIGH ORDER FOR EXTREME PROBLEMS OF DIFFERENTIAL INCLUSIONS
Author(s) -
М. А. Садыгов
Publication year - 2021
Publication title -
chronos journal
Language(s) - English
Resource type - Journals
ISSN - 2658-7556
DOI - 10.52013/2658-7556-52-2-17
Subject(s) - lipschitz continuity , differential inclusion , mathematics , penalty method , banach space , mathematical analysis , order (exchange) , perturbation (astronomy) , mathematical optimization , physics , finance , quantum mechanics , economics
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 − (, , , , ) 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 − (, , , , ) locally Lipschitz conditions.