Well-posedness for the optimistic counterpart of uncertain vector optimization problems

In this article, we consider vector optimization problems with uncertain data. We first formulate optimistic counterparts of the reference problems and propose concepts of efficient solutions to such counterparts. We then introduce concepts of pointwise and global well-posedness for optimistic counterparts. Using the generalized Gerstewitz's function and properties of elements in the image space, we establish the relationships between well-posedness properties for the reference problems and that for scalar optimization ones. Based on such relations, we have studied sufficient conditions of these well-posedness properties for the considered problems via the corresponding scalar problems. Finally, by virtue of a forcing function, the characterizations of the two concepts of well-posedness for such problems are presented.