@Article{Idczak2014,
author = "Idczak, Dariusz and Walczak, Stanislaw",
title = "Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "4",
pages = "763--775",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.4.763",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.4.763",
abstract = "In the paper, we study a linear-quadratic optimal control problem of Mayer type given by a fractional control system. First, we prove a theorem on the existence of a solution to such a problem. Next, using the local implicit function theorem, we derive a formula for the gradient of a cost functional under constraints given by a control system and prove a maximum principle in the case of a control constraint set. The formula for the gradient is used to implement the gradient methods for the problem under consideration.",
keywords = "fractional Riemann-Liouville derivative, Mayer problem, existence of an optimal solution, maximum principle, gradient method",
issn = "1232-9274"
}