On weakly efficient bounds for multiple objective programming problems

In this paper we analyze the consequences produced by introducing the notions of weakly efficient bounds and suprema in the multiple objective programming model. These concepts can be seen as generalizations of their scalar counterparts and some properties and results concerning them are obtained. Through the developed theory it is shown that under certain assumptions, we can get a polarity relation, in a weakly efficient sense, between the multiobjective convex programming problem and the one that arises in computing its weakly efficient suprema. This provides us with a restricted dual weakly vector problem definition for the linear case. Some apparently new theorems of the alternative given in this work have special relevance in this issue.