Fenchel equalities and bilinear minmax equalities - Greco, G.H.; Flores-Franulic, A.; Román-Flores, H. (Mathematica Scandinavica, 2006)
Chief objects here are pairs (X,F) of convex subsets in a Hilbert space, satisfying the bilinear minmax equality 26737 _xX_yF x,y=_yF_xX x,y. 26737 Specializing F to be an affine closed subspace we recover and restate crucial concepts of convex duality, revolving around Fenchel equalities, biconjugation, and inf-convolution. The resulting perspective reinforces the strong links between minmax, set-theoretic, and functional aspects of convex analysis.