16 citations · 42 across the 20 of their papers we have counts for
6 papers · 1 filter
Perturbed Fenchel duality and first-order methods
David H. Gutman, Javier F. Peña
We show that the iterates generated by a generic first-order meta-algorithm satisfy a canonical perturbed Fenchel duality inequality. The latter in turn readily yields a unified de…
A data-independent distance to infeasibility for linear conic systems
Javier Pena, Vera Roshchina
We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric…
An algorithm to compute the Hoffman constant of a system of linear constraints
Javier Pena, Juan Vera, Luis Zuluaga
We propose a combinatorial algorithm to compute the Hoffman constant of a system of linear equations and inequalities. The algorithm is based on a characterization of the Hoffman c…
Computational performance of a projection and rescaling algorithm
Javier Pena, Negar Soheili
This paper documents a computational implementation of a {\em projection and rescaling algorithm} for finding most interior solutions to the pair of feasibility problems \[ \text{f…
The condition of a function relative to a polytope
David H. Gutman, Javier F. Pena
The condition number of a smooth convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In pa…
Convergence rates of proximal gradient methods via the convex conjugate
David H. Gutman, Javier F. Pena
We give a novel proof of the and convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The cru…