Numerische Mathematik

, Volume 19, Issue 4, pp 341–347 | Cite as

Extension of Newton's method to nonlinear functions with values in a cone

  • Stephen M. Robinson


We show how Newton's method may be extended, using convex optimization techniques, to solve problems of the form
$$Find \bar x such that f(\bar x) \in K$$
, 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.


Mathematical Method Optimization Technique Nonlinear Function Convergence Result Error Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Stephen M. Robinson
    • 1
  1. 1.Mathematics Research CenterUniversity of WisconsinMadisonUSA

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