A certificate for semidefinite relaxations in computing positive dimensional real varieties

2012/12/20 by Yue Ma, Ma, Yue, Chu Wang +3 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.OC

paper · pdf · doi:10.48550/arxiv.1212.4924

21 pages

arxiv created 2012/12/20 · arxiv updated 2012/12/21

Abstract

For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal J generated by the kernel of a truncated moment matrix and nesting between I and its real radical ideal. We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic delta-regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations.

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