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arXiv · 1404.5489

Border Basis relaxation for polynomial optimization

Marta Abril Bucero·Bernard Mourrain
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Abstract

A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to detect when the relaxation sequence reaches the minimum, using a sparse flat extension criterion. We also provide a new algorithm to reconstruct a finite sum of weighted Dirac measures from a truncated sequence of moments, which can be applied to other sparse reconstruction problems. As an application, we obtain a new algorithm to compute zero-dimensional minimizer ideals and the minimizer points or zero-dimensional G-radical ideals. Experimentations show the impact of this new method on significant benchmarks.

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Marta Abril Bucero, Bernard Mourrain. 2015-08-22. Border Basis relaxation for polynomial optimization. https://arxiv.org/abs/1404.5489

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