Chief objects here are pairs (X, F ) of convex subsets in a Hilbert space, satisfying the bilinear minmax equality inf_{x\in X} sup_{y\in Y}\langle x, y \rangle = sup_{y\in Y} inf_{x\in X} \langle x, y\rangle. 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.
Fenchel equalities and bilinear minmax equalities
Greco, Gabriele Hans;
2006-01-01
Abstract
Chief objects here are pairs (X, F ) of convex subsets in a Hilbert space, satisfying the bilinear minmax equality inf_{x\in X} sup_{y\in Y}\langle x, y \rangle = sup_{y\in Y} inf_{x\in X} \langle x, y\rangle. 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.File in questo prodotto:
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