2008/09/10 by Didier Henrion, Henrion, Didier
Engineering · Mathematics · #14H50 #90C22 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematics and Applications #Optimization and Control (math.OC) #math.OC #msc:14H50 #msc:90C22
paper · pdf · doi:10.48550/arxiv.0809.1826
openalex publication_date 2008/09/10 · arxiv created 2008/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex hull of a plane quartic to be exactly semidefinite representable with at most 12 lifting variables. If the quartic is rationally parametrizable, an exact semidefinite representation with 2 lifting variables can be obtained. Various numerical examples illustrate the techniques and suggest further research directions.