Chief objects here are pairs (X, F) of convex subsets in a Hilbert space, satisfying the bilinear minmax equality inf sup [x, y] = sup inf [x, y] 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.
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