ABSTRACT
Let G be a non-empty subset of a (real) locally convex space F and h: https://www.w3.org/1998/Math/MathML"> F → R ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003065098/b1b9c184-4054-4965-b4a1-a7c1424a86f6/content/ieq0029.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> a functional. We show that the conditions of existence of functionals ψ∈F* , ψ ≠ 0, which support G and separate G from certain level sets of h, closedly or openly or nicely (in the sense of V. Klee [7]) imply duality formulae which reduce the computation of inf h(G) to the computation of the infima of h on some closed half-spaces or strips or closed strips containing G and that, conversely, under some additional connectedness assumptions on G and certain level sets of h, these support and separation conditions are also necessary for our duality formulae to hold.
