Best $\ell_1$-approximation of nonnegative polynomials by sums of squares

TL;DR

This paper derives an explicit formula for the best -norm approximation of a nonnegative polynomial by sums of squares of a specified degree, advancing approximation techniques in polynomial optimization.

Contribution

It introduces a novel explicit expression for the best -norm approximation of nonnegative polynomials by sums of squares.

Findings

Provides explicit formula for approximation

Enhances polynomial optimization methods

Improves understanding of polynomial approximation

Abstract

Given a nonnegative polynomial f, we provide an explicit expression for its best $\ell_1$-norm approximation by a sum of squares of given degree.