yuanchenyang/lean_low_rank_univariate_sos
A Lean 4 formalization of the main theorem of Legat, Yuan and Parrilo, "Low-Rank Univariate Sum of Squares Has No Spurious Local Minima" (SIAM J. Optim. 33(3), 2023). For a real univariate polynomial p and a pair of polynomials u = (u₁, u₂), consider the quadratically penalized Burer–Monteiro objective f_p(u) = ‖σ(u) - p‖² with σ(u) = u₁² + u₂², the norm coming from any inner product on ℝ[x]. The formalized theorem states that if p is a sum of two squares (which is the case for any nonnegative univariate polynomial) and u is a second-order critical point of f_p (vanishing gradient and…
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