Weak duality theorem about multi-objective linear vector optimization with set-valued constraint

The duality theory is the basic theory for mathematical planning in which the study of weak duality theorem under different controlling conditions is an important part of duality theorem research.Document discusses the weak duality theorem and the strong duality theorem of linear vector optimization with single value constraint.With the set-value duality theory,this paper demonstrates the weak duality theorem of linear vector optimization with set-valued constraint and reaches the similar conclusion with that in document \.At the same time it proves a few formulae which are equal to the weak duality theorem.Thus we generalized and completed the duality theory.