Nonsymmetric Conic Optimization and Dual Certificates for Sums-of-Squares

In this 49-minute lecture, Dávid Papp from North Carolina State University explores "Nonsymmetric conic optimization and dual certificates for sums-of-squares" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Discover alternative approaches to the conventional semidefinite programming (SDP) formulation of sums-of-squares (SOS) optimization problems, which typically require a quadratic number of auxiliary variables and suffer from ill-conditioning. Learn about nonsymmetric conic optimization methods that reduce complexity, and how these can be combined with polynomial interpolation to improve conditioning and computational efficiency. Explore how explicit SOS decompositions can still be computed efficiently despite circumventing the SDP formulation, and understand how rigorous rational nonnegativity certificates can be derived directly from numerical calculations. Recorded on May 19, 2025, this presentation is part of the Institute for Pure & Applied Mathematics (IPAM) workshop series at UCLA.