Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 55, Issue 8, Pages -Publisher
AIP Publishing
DOI: 10.1063/1.4890292
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Funding
- NSF [PHY-0803371]
- ARO [W911NF-09-1-0442]
- DOE [DE-FG03-92-ER40701]
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development and Innovation
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Given an operator convex function f(x), we obtain an operator-valued lower bound for cf(x) + (1 - c) f(y) - f(cx + (1 - c) y), c is an element of[0, 1]. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false for functions that are convex but not operator convex. (C) 2014 AIP Publishing LLC.
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