This paper studies the issue of well-posedness
for vector optimization. It is shown that
coercivity implies well-posedness without any convexity assumptions
on problem data.
For
convex vector optimization problems,
solution sets of such problems are non-convex in general,
but they are highly structured.
By exploring such structures carefully via convex analysis,
we are able to obtain
a number of positive results, including a criterion for well-posedness
in terms of that of associated scalar problems.
In particular
we show that a well-known relative interiority condition
can be used as a sufficient condition for well-posedness in convex
vector optimization.