Data loci in algebraic optimization

TL;DR

This paper introduces methods and algorithms to identify parameter conditions in algebraic optimization problems that ensure the existence of local minima or maxima satisfying specific polynomial properties.

Contribution

It provides new examples, methods, and algorithms for analyzing parametric optimization problems with polynomial conditions on solutions.

Findings

Algorithms for determining parameter conditions

Examples of algebraic optimization problems

Conditions ensuring solutions meet polynomial criteria

Abstract

In this article we provide examples, methods and algorithms to determine conditions on the parameters of certain type of parametric optimization problems, such that among the resulting local minima and maxima there is at least one which satisfies given polynomial conditions (for example it is singular or symmetric).