Comment on "Approximation algorithms for quadratic programming"

TL;DR

This paper corrects a mathematical error in the radius calculation of the Dikin ellipsoid for intersecting ellipsoids, leading to an updated approximation bound for certain quadratic programming problems.

Contribution

It provides a correction to the radius formula and the approximation bound in the context of convex and nonconvex quadratic programs.

Findings

Corrected the radius of the Dikin ellipsoid from m to √(m^2 + m)

Updated the approximation bound for quadratic programming problems

Clarified the impact of the correction on previous results

Abstract

The radius of the outer Dikin ellipsoid of the intersection of $m$ ellipsoids due to Fu et al. (J. Comb. Optim., 2, 29-50, 1998) is corrected from $m$ to $\sqrt{m^2+m}$. The approximation bound for the general convex quadratic constrained nonconvex quadratic program is correspondingly corrected.