  In the present paper, several types of efficiency conditions are established
for vector optimization problems with cone constraints affected by uncertainty,
but with no information of stochastic nature about the uncertain data.
Following a robust optimization approach, data uncertainty is faced by handling
set-valued inclusion problems. The employment of recent results about error
bounds and tangential approximations of the solution set to the latter enables
one to achieve necessary conditions for weak efficiency via a penalization
method as well as via the modern revisitation of the Euler-Lagrange method,
with or without generalized convexity assumptions. The presented conditions are
formulated in terms of various nonsmooth analysis constructions, expressing
first-order approximations of mappings and sets, while the metric increase
property plays the role of a constraint qualification.
