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An algorithm to compute the Hoffman constant of a system of linear constraints

Javier Pena(jfp***at***andrew.cmu.edu)
Juan Vera(j.c.veralizcano***at***uvt.nl)
Luis Zuluaga(luis.zuluaga***at***lehigh.edu)

Abstract: 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 constant as the largest of a finite canonical collection of easy-to-compute Hoffman constants. Our algorithm and characterization extend to the more general context where some of the constraints are easy to satisfy as in the case of box constraints. We highlight some natural connections between our characterizations of the Hoffman constant and Renegar's distance to ill-posedness for systems of linear constraints.

Keywords: Hoffman constant, surjective mappings, norms

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Combinatorial Optimization (Polyhedra )


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Entry Submitted: 04/23/2018
Entry Accepted: 04/23/2018
Entry Last Modified: 04/23/2018

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