Whitney's Theorem, Triangular Sets and Probabilistic Descent on Manifolds
Optimization and Control
2018-08-28 v1 Algebraic Geometry
Differential Geometry
Abstract
We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us to work in a reduced dimensional embedding space. A numerical continuation method applied to the reduced-dimensional embedded manifold is used to drive the procedure.
Cite
@article{arxiv.1808.08548,
title = {Whitney's Theorem, Triangular Sets and Probabilistic Descent on Manifolds},
author = {David W. Dreisigmeyer},
journal= {arXiv preprint arXiv:1808.08548},
year = {2018}
}