Whitney’s Theorem, Triangular Sets, and Probabilistic Descent on Manifolds

David W. Dreisigmeyer ()
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David W. Dreisigmeyer: United States Census Bureau

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 4, 935-946

Abstract: 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.

Keywords: Probabilistic descent; Manifold; Nonlinear optimization; 65K10; 90C56 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01508-9

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