Monomial Sphere Maps and Linear Programming

Abstract

This chapter continues our investigation of the linear systems for monomial sphere maps. Since the number of examples tends to infinity as the degree increases, we consider methods for restricting the collection of examples. We do so by considering the problem from the perspective of linear programming. The results in this chapter concern two optimization problems. In Section 2, we introduce a natural minimization problem; we wish to minimize the sum of the coefficients of polynomials in a certain collection. We also study sparse solutions, those that minimize the number of terms in such polynomials for a given degree.