Improving SDP bounds for minimizing quadratic functions over the l1-ball
Optimization and Control
2007-05-23 v2
Abstract
In this note, we establish superiority of the so-called copositive bound over a bound suggested by Nesterov for the quadratic problem to minimize a quadratic form over the l1-ball. We illustrate the improvement by simulation results. The copositive bound has the additional advantage that it can be easily extended to the inhomogeneous case of quadratic objectives including a linear term. We also indicate some improvements of the eigenvalue bound for the quadratic optimization over the lp-ball with 1<p<2, at least for p close to one.
Cite
@article{arxiv.math/0503174,
title = {Improving SDP bounds for minimizing quadratic functions over the l1-ball},
author = {Immanuel M. Bomze and Florian Frommlet and Martin Rubey},
journal= {arXiv preprint arXiv:math/0503174},
year = {2007}
}
Comments
12 pages, 4 figures, v2: Figure 2a corrected, minor changes