Algebraic Geometry in Optimization Theory
Abstract
This essay traces the historical development of optimization, focusing on one-variable problems and their applications. We discuss the role of non-negative polynomials in optimization and carefully examine a classical result by Motzkin. Building on this result, we construct a new polynomial that is non-negative but not a sum-of-squares polynomial, propose a method to check whether a polynomial is sum-of-squares, and explore the relationship between the set of sum-of-squares polynomials and the set of non-negative polynomials.
Fields of Study & Subjects
Advanced Optimization Algorithms Research
Polynomial and algebraic computation
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Theoretical and Natural Science
- Volume
- 156
- Issue
- 1
- Pages
- 42–54
- Publication date
- 10 February 2026
- Language
- EN