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Explore the cutting-edge advancements in polynomial optimization through this comprehensive conference talk on difference-of-sums-of-squares (D-SOS) and difference-of-convex-sums-of-squares (DC-SOS) decompositions. Delve into these natural extensions of Hilbert's 17th problem, gaining insights into the intrinsic algebraic structures of polynomials. Discover how these techniques provide robust frameworks for tackling complex large-scale polynomial optimization problems within the difference-of-convex (DC) optimization paradigm. Engage with open questions presented to stimulate further research and development in this dynamic field. Learn about the evolving landscape of polynomial optimization and its modern techniques over the course of this one-hour presentation.
