Strong nonnegativity and sums of squares on real varieties

2011/01/04 by Mohamed Omar, Omar, Mohamed, Brian Osserman +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Polynomial and algebraic computation #Tensor decomposition and applications #math.AG #math.OC #msc:13J30 #msc:14P10 #msc:90C22

paper · pdf · doi:10.48550/arxiv.1101.0826

11 pages, 4 figures

arxiv created 2011/10/16 · arxiv updated 2011/10/18

Abstract

Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the property that a sum of squares is strongly nonnegative. We show that this algebraic property is equivalent to nonnegativity for nonsingular real varieties. Moreover, for singular varieties, we reprove and generalize obstructions of Gouveia and Netzer to the convergence of the theta body hierarchy of convex bodies approximating the convex hull of a real variety.

Related

• Sums of Squares and Sparse Semidefinite Programming
• Do Sums of Squares Dream of Free Resolutions?
• Nonnegativity certificates on real algebraic surfaces
• On sum of squares certificates of non-negativity on a strip
• Sums of squares representations on singular loci