Extension of Newton's method to nonlinear functions with values in a cone
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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.
$$Find \bar x such that f(\bar x) \in K$$
KeywordsMathematical Method Optimization Technique Nonlinear Function Convergence Result Error Bound
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