The optimality principle for second-order discrete and discrete-approximate inclusions The optimality principle for second-order discrete and discrete-approximate inclusions

• Published in: An international journal of optimization and control Vol. 11; no. 2; pp. 206 - 215
• Main Author: Demir Sağlam, Sevilay
• Format: Journal Article
• Language: English
• Published: Balikesir Prof. Dr. Ramazan Yaman 01-01-2021; Balikesir University, Faculty of Engineering Department of Industrial Engineering; Balikesir University
• Subjects: Approximation; Discrete inclusion; Equivalence; Inclusions; locally adjoint mapping; Mathematical analysis; Mayer problem; Mühendislik; optimality condition; Optimization; İstanbul; Türkiye; Optimality condition; Discrete inclusion; Approximation; Locally adjoint mapping
• ISSN: 2146-0957; 2146-5703
• DOI: 10.11121/ijocta.01.2021.001056

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.