Let (Xd , Xd ) be a real normed space, and let (Xc, Xc ) be a reflexive
real Banach space. Let the set Sd ⊂ Xd consist of finitely many elements, and
let Sc ⊂ Xc be a nonempty, convex, closed and bounded set. Moreover, let
the functional f : Sd × Sc → R have the property that for every xd ∈ Sd
the functional f (xd , ) is continuous and quasiconvex. Prove that the discretecontinuous optimization problem
is solvable.
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