Global Optimization via the Dual SONC Cone and Linear Programming

Explore global optimization techniques using the dual SONC cone and linear programming in this 36-minute conference talk from the Fields Institute's Workshop on Real Algebraic Geometry and Algorithms for Geometric Constraint Systems. Delve into Mareike Dressler's research on minimizing exponential sums and multivariate real polynomials through a relaxation approach. Learn about the dual cone of sums of nonnegative circuits (SONC), its containment in the primal cone as a nonnegativity certificate, and how membership in the dual cone can be verified using linear programming. Examine key concepts such as zignomials, circuit functions, and global optimization techniques. Gain insights from numerical examples and compare this method to existing approaches in this comprehensive exploration of advanced mathematical optimization techniques.

Introduction
Zignomials
Nonnegativity certificates
Key idea
Introduction to circuit functions
Circuit functions
Nonnegativity
Dual SONC
Checking Membership
Global Optimization
Linear Programming
Numerical Examples
Takehome message
Question
Summary