Optimality conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions

✍ Scribed by Tadeusz Antczak

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 753 KB
• Volume: 225
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.07.028

✦ Synopsis

weak) Pareto optimal solution d-r-type I objective and constraint functions Optimality conditions Duality a b s t r a c t

In this paper, new classes of nondifferentiable functions constituting multiobjective programming problems are introduced. Namely, the classes of d-r-type I objective and constraint functions and, moreover, the various classes of generalized d-r-type I objective and constraint functions are defined for directionally differentiable multiobjective programming problems. Sufficient optimality conditions and various Mond-Weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type. Finally, it is showed that the introduced d-r-type I notion with r = 0 is not a sufficient condition for Wolfe weak duality to hold. These results are illustrated in the paper by suitable examples.