Multiobjective programming under (φ, d)-V-type I univexity

Abstract

In this paper, we have introduced a new class of (φ, d)-V-type I univex, quasi (φ, d)-V-type I univex, pseudo (φ, d)-V-type I univex, quasi-pseudo (φ, d)-V-type I univex and pseudo-quasi (φ, d)-V-type I univex functions in case of nonlinear multiobjective programming problem where functions involved are nondifferentiable and illustrated through non-trivial examples that this class extends some known classes in literature. Various Karush-Kuhn-Tucker type sufficient optimality conditions are obtained under this newly introduced class of functions. Also, for mixed type multiobjective dual program, we have established weak, strong, converse and strict converse duality results in order to relate the efficient and weak efficient solutions of primal and dual problem.