Dontchev, Asen L. Uniform convergence of the Newton method for Aubin continuous maps. (English) Zbl 0865.90115 Serdica Math. J. 22, No. 3, 385-398 (1996). Summary: We prove that the Newton method applied to the generalized equation \(y\in f(x)+F(x)\) with a \(C^1\) function \(f\) and a set-valued map \(F\) acting in Banach spaces, is locally convergent uniformly in the parameter \(y\) if and only if the map \((f+F)^{-1}\) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform \(Q\)-quadratic convergence provided that the derivative of \(f\) is Lipschitz continuous. As an application, we give a characterization of the uniform local \(Q\)-quadratic convergence of the sequential quadratic programming method applied to a perturbed nonlinear program. Cited in 1 ReviewCited in 25 Documents MSC: 90C30 Nonlinear programming 49M37 Numerical methods based on nonlinear programming 65K10 Numerical optimization and variational techniques 47H04 Set-valued operators Keywords:Aubin continuity; sequential quadratic programming; perturbed nonlinear program PDFBibTeX XMLCite \textit{A. L. Dontchev}, Serdica Math. J. 22, No. 3, 385--398 (1996; Zbl 0865.90115) Full Text: EuDML