Second-order optimality conditions for efficiency in C1,1-smooth quasiconvex multiobjective programming problem

• Published in: Computational & applied mathematics Vol. 40; no. 6
• Main Authors: Su, Tran Van, Hang, Dinh Dieu
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical functions; Mathematical programming; Mathematics; Mathematics and Statistics; 90C46; Smooth quasiconvex multiobjective programming problem with constraints; 49J52; Second-order Mordukhovich/Fréchet Subdifferentials; Second-order optimality conditions; 90C29; Weak Efficiency; Generalized second-order Ben-Tal constraint qualifications; 49K27
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-021-01625-0

This paper deals with a quasiconvex multiobjective programming problem with inequality and set constraints with C 1 , 1 -smooth data. Based on the definition of quasiconvexity, pseudoconvexity and second-order Mordukhovich/Fréchet subdifferentials of extended-real-valued function, we propose the two generalized Ben-Tal second-order constraint qualifications and then establish strong and weak Karush-Kuhn-Tucker type second-order necessary optimality conditions for weak efficiency to such problem. Under some suitable assumptions on the pseudoconvexity and C 1 , 1 -around a feasible solution of objective and constraint functions, some second-order sufficient optimality conditions in terms of Fréchet subdifferentials are presented. An application of the result on sufficient optimality of order two in terms of Mordukhovich subdifferentials in the sense of the functions belong to C 2 -around a feasible solution is obtained. Some examples are also provided to demonstrate for our findings.