Fenchel equalities and bilinear minmax equalities

Authors

  • G.H. Greco
  • A. Flores-Franulic
  • H. Román-Flores

DOI:

https://doi.org/10.7146/math.scand.a-14992

Abstract

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.

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Published

2006-06-01

Issue

Vol. 98 No. 2 (2006)

Section

Articles

How to Cite

[1]
G. Greco, A. Flores-Franulic, and H. Román-Flores, “Fenchel equalities and bilinear minmax equalities”, Math. Scand., vol. 98, no. 2, pp. 217–228, Jun. 2006, doi: 10.7146/math.scand.a-14992.