Slaters condition and boundary solution Slater's condition is a sufficient condition for a convex optimization problem to satisfy strong duality. It says that feasible region should have an interior. My question is suppose I have a convex optimization problem which satisfies slater's condition, then can a boundary point be the optima of such a problem, or does slater's also want the optima to be in the interior?

No. It's possible for Slater's condition to be satisfied and the only optimal solution is on the boundary of the feasible region. It's also possible to have Slater's condition be satisfied with the only optimal solution on the interior of the feasible region. Examples are pretty easy to construct.