A nonspectrahedral hyperbolicity cone
Source: github.com/openai/math/tree/main/preprints/A-Nonspectrahedr…
We construct a homogeneous polynomial of degree 16 in 23 real variables whose hyperbolicity cone has no representation by a finite homogeneous real symmetric linear matrix inequality. This disproves the geometric Generalized Lax conjecture.
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The generalized Lax conjecture was a central topic of study in the field of hyperbolic polynomials. Hyperbolic polynomials in general serve as a bridge between the seemingly disparate fields of algebraic geometry and convex optimization, as each hyperbolic polynomial gives rise in a natural way to…