Existence and discrete approximation for optimization problems governed by fractional differential equations

•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 di...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 59; pp. 338 - 348
Main Authors: Bai, Yunru, Baleanu, Dumitru, Wu, Guo–Cheng
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.06.2018
Elsevier Science Ltd
Subjects:
Algorithms
Approximation
Convergence
Differential equations
Existence theorems
Fixed points (mathematics)
Fractional differential optimization problem
Mathematical analysis
Nonlinear programming
Numerical approximation algorithm
Optimization
Studies
Weak Carathéodory solution
Weierstrass existence theorem
Numerical approximation algorithm
Weierstrass existence theorem
Weak Carathéodory solution
Fractional differential optimization problem
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:•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.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.11.009