Blenders

2010/08/26 by Bruce Reznick, Reznick, Bruce · 1 citation
Computer Science · Mathematics · #11E25 #11E76 #11P05 #14P99 #26B25 #52A41 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1008.4533

openalex publication_date 2010/08/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

A blender is a closed convex cone of real homogeneous polynomials that is also closed under linear changes of variable. Non-trivial blenders only occur in even degree. Examples include the cones of psd forms, sos forms, convex forms and sums of 2u-th powers of forms of degree v. We present some general properties of blenders and analyze the extremal elements of some specific blenders.

Cited by

• Convexity and SOS-Convexity of Sum of Separable and Biquadratic Quartic Polynomials and Optimization

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