Showing papers in "Ricerche Di Matematica in 2002"
Journal Article•
TL;DR: In this article, the existence of a sequence (xk) satisfying 0 ∈ f(xk)+∇f(x k) + ∇k+1−xk + 2∇2f(k)2 + G(k + 1 − xk) + 2 ∇2k+2k 2 + g(k+ 1 − k) 2 + k + 2k + k+1 − k + 1 2∆k + ∆k 2+g(k))2 + k.
Abstract: . We investigate the existence of a sequence (xk) satisfying 0 ∈ f(xk)+∇f(xk)(xk+1− xk) + 2∇2f(xk)(xk+1 − xk)2 + G(xk+1) and converging to a solution x∗ of the generalized equation 0 ∈ f(x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces. We show that the previous sequence is locally superquadratic convergent to x∗ whenever ∇2f satisfies a Holder-type condition and the set-valued map [f(x∗)+∇f(x∗)(· −x∗)+ 1 2∇f(x)(· −x∗)2+G(·)]−1 is M -pseudo-Lipschitz around (0, x∗).
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