Optimality for (h,φ)-multiobjective programming involving generalized type-I functions

Abstract

Based upon Ben-Tal's generalized algebraic operations, new classes of functions, namely (h,?)-type-I, quasi (h,?)-type-I, and pseudo (h,?)-type-I, are defined for a multi-objective programming problem. Sufficient optimality conditions are obtained for a feasible solution to be a Pareto efficient solution for this problem. Some duality results are established by utilizing the above defined classes of functions, considering the concept of a Pareto efficient solution.