Existence and discrete approximation for optimization problems governed by fractional differential equations - Bai, Yunru; Baleanu, Dumitru; Wu, Guo–Cheng (Communications in nonlinear science & numerical simulation, 2018)
•A class of generalized differential optimization problems driven by the Caputo derivative is studied.•The existence of weak Caratheodory solution for DOP is obtained.•A numerical approximation algorithm is introduced and a convergence theorem is established. We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.