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

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

Authors

DOI:

https://doi.org/10.11121/ijocta.01.2021.001056

Keywords:

Discrete inclusion, approximation, locally adjoint mapping, optimality condition

Abstract

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.

Author Biography

Sevilay Demir Sağlam, Department of Mathematics, University of Istanbul, Turkey

is currently working as a research assistant at the Department of Mathematics, Istanbul University, Istanbul, Turkey. She received M.Sc. and Ph.D. degrees from the Department of Mathematics, Istanbul University in 2012 and 2017, respectively. Her current research interests are the polyhedral optimization, control theory, duality theory and the conditions of optimality for discrete and differential inclusions given by set-valued mappings.

References

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Published

2021-05-26

How to Cite

Demir Sağlam, S. (2021). The optimality principle for second-order discrete and discrete-approximate inclusions: The optimality principle for second-order discrete and discrete-approximate inclusions. An International Journal of Optimization and Control: Theories &Amp; Applications (IJOCTA), 11(2), 206–215. https://doi.org/10.11121/ijocta.01.2021.001056

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Research Articles