Existence and Discrete Approximation for Optimization Problems Governed by Fractional Differential Equations

Abstract

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Caratheodory 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. (C) 2017 Elsevier B.V. All rights reserved.