The continuous Newton-Raphson method can look ahead

This paper is about an intriguing property of the continuous Newton-Raphson method for the minimization of a continuous objective function f: if x is a point in the domain of attraction of a strict local minimizer x* then the flux line of the Newton-Raphson flow that starts in x approaches x* from a direction that depends only on the behavior of f in arbitrarily small neighborhoods around x and x*. In fact, if F is a sufficiently benign perturbation of f on an open region D not containing x, then the two flux lines through x defined by the Newton-Raphson vector fields that correspond to f and F differ from one another only within D.\ud \ud The work was supported by EPSRC grant GR/S34472 (R. Hauser) and by the Clarendon Fund, Oxford University Press and ORS Award, Universities UK (J Nedic

Newton's method for the general parametric center problem with applications

"March, 1991."Includes bibliographical references (p. 37-39).Kok Choon Tan and Robert M. Freund

Newton's method for the general parametric center problem with applications

"March, 1991."Includes bibliographical references (p. 37-39).Kok Choon Tan and Robert M. Freund