Whitney's theorem, triangular sets, and probabilistic descent on manifolds (Q2322361)

This article studies doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. Whitney's theorem offers a potentially large decrease in the effective dimension one needs to optimize. But, firstly, the decrease in dimensionality is achieved by a linear projection from the initial ambient space into a lower-dimensional working space. Secondly, the reconstruction from the reduced dimension working space back into the original space is generally nonlinear. A numerical method, based on application of Whitney's theorem, applied to the reduced-dimensional manifold is given to present the procedure.