Optimality conditions for higher order polyhedral discrete and differential inclusions

Author:

Demir Sağlam Sevilay1,Mahmudov Elimhan2

Affiliation:

1. Istanbul University, Department of Mathematics, Istanbul, Turkey

2. Istanbul Technical University, Department of Mathematics, Istanbul, Turkey + Azerbaijan National Academy of Sciences, Institute of Control Systems, Baku, Azerbaijan

Abstract

The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.

Publisher

National Library of Serbia

Subject

General Mathematics

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