Fenchel equalities and bilinear minmax equalities

• Autores: G. H. Greco, A. Flores, H. Román Flores
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 98, Nº 2, 2006, págs. 217-228
• Idioma: inglés
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• Resumen

  • Chief objects here are pairs $(X,F)$ of convex subsets in a Hilbert space, satisfying the bilinear minmax equality 26737 \inf_{x\in X}\sup_{y\in F} \langle x,y\rangle=\sup_{y\in F}\inf_{x\in X} \langle x,y\rangle. 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.