TY  - JOUR
ID  - Idczak2014
LB  - Idczak2014
AU  - Idczak, Dariusz
AU  - Walczak, Stanislaw
TI  - Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods
ST  - Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 4
SP  - 763
EP  - 775
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.4.763
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.4.763
AB  - 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.
KW  - fractional Riemann-Liouville derivative
KW  - Mayer problem
KW  - existence of an optimal solution
KW  - maximum principle
KW  - gradient method
SN  - 1232-9274
ER  -