Approximate Subdifferential of the Difference of Two Vector Convex Mappings
Abdelghali Ammar,
Mohamed Laghdir,
Ahmed Ed-dahdah,
Mohamed Hanine
Affiliations
Abdelghali Ammar
Department of Computer Engineering, Networks and Telecommunications, National School of Applied Sciences, Cadi Ayyad University, BP. 63, Safi 46000, Morocco
Mohamed Laghdir
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, BP. 20, El Jadida 24000, Morocco
Ahmed Ed-dahdah
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, BP. 20, El Jadida 24000, Morocco
Mohamed Hanine
Department of Telecommunications, Networks, and Informatics, National School of Applied Sciences, Chouaib Doukkali University, El Jadida 24000, Morocco
This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem.
