Optimization of Polynomials with Sparsity Encoded in a Few Linear Forms

TL;DR

This paper presents methods to optimize polynomials with sparsity in a few linear forms, including detection and approximation techniques, enabling efficient optimization on specific domains like spheres and polytopes.

Contribution

It introduces a novel approach to exploit polynomial sparsity in linear forms for optimization, detection, and approximation.

Findings

Efficient optimization of sparse polynomials on spheres and polytopes.

A simple procedure to detect sparsity in polynomials.

Method to approximate general polynomials by sparse ones.

Abstract

We consider polynomials of a few linear forms and show how exploit this type of sparsity for optimization on some particular domains like the Euclidean sphere or a polytope. Moreover, a simple procedure allows to detect this form of sparsity and also allows to provide an approximation of any polynomial by such sparse polynomials.