16 citations · 42 across the 20 of their papers we have counts for
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Equivalence and invariance of the chi and Hoffman constants of a matrix
Javier F. Pena, Juan C. Vera, Luis F. Zuluaga
We show that the following two condition measures of a full column rank matrix are identical: the chi constant and a signed Hoffman constant. This id…
New characterizations of Hoffman constants for systems of linear constraints
Javier Pena, Juan Vera, Luis Zuluaga
We give a characterization of the Hoffman constant of a system of linear constraints in {\em relative} to a {\em reference polyhedron} . The reference polyhe…
Generalized conditional subgradient and generalized mirror descent: duality, convergence, and symmetry
Javier Pena
We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \;…
The condition number of a function relative to a set
David H. Gutman, Javier F. Pena
The condition number of a differentiable convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the functio…