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A Semidefinite Programming Method for Integer Convex Quadratic Minimization
April 28, 2015 Β· Declared Dead Β· π Optimization Letters
"No code URL or promise found in abstract"
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Authors
Jaehyun Park, Stephen Boyd
arXiv ID
1504.07672
Category
math.OC: Optimization & Control
Cross-listed
cs.DS
Citations
59
Venue
Optimization Letters
Last Checked
5 months ago
Abstract
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the problem. By interpreting the solution to the SDP relaxation probabilistically, we obtain a randomized algorithm for finding good suboptimal solutions, and thus an upper bound on the optimal value. The effectiveness of the method is shown for numerical problem instances of various sizes.
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