Modulus of convexity for operator convex functions
Abstract
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 ∈ [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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 21, 2014
- Source ID
- 10.1063/1.4890292
Entities
People
- Isaac H. Kim
Organizations
- Army Research Office
- National Science Foundation
- United States Department of Energy