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...



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.



May 26, 2022
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