Improving SDP bounds for minimizing quadratic functions over the l1-ball

Details Improving SDP bounds for minimizing quadratic functions over the l1-ball Improving SDP bounds for minimizing quadratic functions over the l1-ball

2005-03-09

arxiv.org/abs/math/0503174v2

Mathematics

Optimization and Control

12 pages, 4 figures, v2: Figure 2a corrected, minor changes

Scientific paper

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

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