scholarly journals Non-linear pricing by convex duality

Automatica ◽  
2015 ◽  
Vol 53 ◽  
pp. 369-375 ◽  
Author(s):  
Mustafa Ç. Pınar
Keyword(s):  
Convex Duality ◽  
Non Linear

On Quasi-Convex Duality

1990 ◽  
Vol 15 (4) ◽  
pp. 597-625 ◽  
Author(s):  
Jean-Paul Penot ◽  
Michel Volle
Keyword(s):  
Convex Duality

scholarly journals Convex duality and uniqueness for BV-minimizers

2015 ◽  
Vol 268 (10) ◽  
pp. 3061-3107 ◽  
Author(s):  
Lisa Beck ◽  
Thomas Schmidt
Keyword(s):  
Convex Duality

scholarly journals Fenchel equalities and bilinear minmax equalities

2006 ◽  
Vol 98 (2) ◽  
pp. 217 ◽  
Author(s):  
G.H. Greco ◽  
A. Flores-Franulic ◽  
H. Román-Flores
Keyword(s):  
Hilbert Space ◽  
Convex Analysis ◽  
Closed Subspace ◽  
Convex Duality ◽  
Functional Aspects ◽  
Convex Subsets

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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