IndicatorLpUnitBall.convex_conj

property IndicatorLpUnitBall.convex_conj

The conjugate functional of IndicatorLpUnitBall.

The convex conjugate functional of an Lp norm, p < infty is the indicator function on the unit ball defined by the corresponding dual norm q, given by 1/p + 1/q = 1 and where q = infty if p = 1 [Roc1970]. By the Fenchel-Moreau theorem, the convex conjugate functional of indicator function on the unit ball in Lq is the corresponding Lp-norm [BC2011].

References

[Roc1970] Rockafellar, R. T. Convex analysis. Princeton University Press, 1970.

[BC2011] Bauschke, H H, and Combettes, P L. Convex analysis and monotone operator theory in Hilbert spaces. Springer, 2011.