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2016

Perturbed sums-of-squares theorem for polynomial optimization and its applications

10 months 20 days ago
Perturbed sums-of-squares theorem for polynomial optimization and its applications
We consider a property of positive polynomials on a compact set with a small perturbation. When applied to a Polynomial Optimization Problem (POP), the property implies that the optimal value of the corresponding SemiDefinite Programming (SDP) relaxation with sufficiently large relaxation order is bounded from below by (f∗ − ) and from above by f∗ + (n + 1), where f∗ is the optimal value of the POP. We propose new SDP relaxations for POP based on modifications of existing sums-of-squares representation theorems. An advantage of our SDP relaxations is that in many cases they are of considerably smaller dimension than those originally proposed by Lasserre. We present some applications and the results of our computational experiments.
Masakazu Muramatsu, Hayato Waki, Levent Tunç
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where OMS
Authors Masakazu Muramatsu, Hayato Waki, Levent Tunçel
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