Newton-Scant method for functions with values in a cone

Abstract : This paper deals with variational inclusions of the form 0 ∈ K − f(x) − g(x) where f is a smooth function from a reflexive Banach space X into a Banach space Y , g is a function from X into Y admitting divided differences and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by a combination of two methods: the Newton and the Secant methods. We show that the order of the semilocal method obtained is equal to (1 + √5)/2. Numerical results are also given to illustrate the convergence at the end of the paper.
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Contributor : Alain Pietrus <>
Submitted on : Monday, January 6, 2014 - 2:21:08 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM

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Alain Pietrus, Célia Jean-Alexis. Newton-Scant method for functions with values in a cone. Serdica Math. J., 2013, 39, pp.271-286. 〈hal-00924150〉

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