Representation of nonnegative convex polynomials

2008/01/24 by Jean B. Lasserre, Lasserre, Jean B. · 1 citation
Computer Science · Mathematics · #14P10 #90C22 #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #Optimization and Control (math.OC) #Polynomial and algebraic computation #math.AG #math.OC #msc:14P10 #msc:90C22

paper · pdf · doi:10.48550/arxiv.0801.3754

openalex publication_date 2008/01/24 · arxiv created 2008/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic subset K of Rn. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define K.

Citations

• Semidefinite Representation of Convex Sets

Cited by

• Hesse's Redemption: Efficient Convex Polynomial Programming

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