Abstract
We show how Newton's method may be extended, using convex optimization techniques, to solve problems of the form
, whereK is a nonempty closed convex cone in a Banach spaceY, andf is a function from a reflexive Banach spaceX intoY. A generalization of the Kantorovich theorem is proved, giving convergence results and error bounds for this method.
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Sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462. An earlier version of this paper was presented to the Fifth Hawaii International Conference on System Sciences, 11–13 January 1972.
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Robinson, S.M. Extension of Newton's method to nonlinear functions with values in a cone. Numer. Math. 19, 341–347 (1972). https://doi.org/10.1007/BF01404880
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DOI: https://doi.org/10.1007/BF01404880