Notes on optimality conditions using Newton diagrams and sums of squares

TL;DR

This paper explores the connections between optimality conditions in polynomial and power series optimization problems, utilizing Newton diagrams and sums of squares techniques.

Contribution

It introduces new insights into how Newton diagrams can be used to analyze sums of squares conditions for optimality.

Findings

Established links between Newton diagrams and sums of squares

Provided criteria for optimality using geometric and algebraic methods

Enhanced understanding of polynomial and power series optimization

Abstract

We consider relationships between optimality conditions using Newton diagrams and sums of squares of polynomials and power series.