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.
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Communicated by Horst Martini.
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Dreisigmeyer, D.W. Whitney’s Theorem, Triangular Sets, and Probabilistic Descent on Manifolds. J Optim Theory Appl 182, 935–946 (2019). https://doi.org/10.1007/s10957-019-01508-9
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DOI: https://doi.org/10.1007/s10957-019-01508-9