Sufficiency and duality in nonsmooth multiobjective programming problem under generalized univex functions (Q469982)

Summary: We consider a nonsmooth multiobjective programming problem where the functions involved are nondifferentiable. The class of univex functions is generalized to a far wider class of \((\varphi, \alpha, \rho, \sigma)\)-\(d_I\)-\(V\)-type I univex functions. Then, through various nontrivial examples, we illustrate that the class introduced is new and extends several known classes existing in the literature. Based upon these generalized functions, Karush-Kuhn-Tucker type sufficient optimality conditions are established. Further, we derive weak, strong, converse, and strict converse duality theorems for Mond-Weir type multiobjective dual program.