Open AccessThe optimality principle for second-order discrete and discrete-approximate inclusions
Author(s) -
Sevilay Demir Sağlam
Publication year - 2021
Publication title -
an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.287
H-Index - 6
eISSN - 2146-5703
pISSN - 2146-0957
DOI - 10.11121/ijocta.01.2021.001056
Subject(s) - differential inclusion , mathematics , equivalence (formal languages) , discrete time and continuous time , nonlinear system , transversality , differential (mechanical device) , order (exchange) , mathematical optimization , mathematical analysis , pure mathematics , statistics , physics , finance , quantum mechanics , engineering , economics , aerospace engineering
This paper deals with the necessary and sufficient conditions of optimality for the Mayer problem of second-order discrete and discrete-approximate inclusions. The main problem is to establish the approximation of second-order viability problems for differential inclusions with endpoint constraints. Thus, as a supplementary problem, we study the discrete approximation problem and give the optimality conditions incorporating the Euler-Lagrange inclusions and distinctive transversality conditions. Locally adjoint mappings (LAM) and equivalence theorems are the fundamental principles of achieving these optimal conditions, one of the most characteristic properties of such approaches with second-order differential inclusions that are specific to the existence of LAMs equivalence relations. Also, a discrete linear model and an example of second-order discrete inclusions in which a set-valued mapping is described by a nonlinear inequality show the applications of these results.