Quadratic convergence of Newton's method for convex interpolation and smoothing

DOI10.1007/s00365-002-0513-2zbMath1014.65011OpenAlexW1491846897MaRDI QIDQ1864181

Liqun Qi, Asen L. Dontchev, Hou-Duo Qi

Publication date: 17 March 2003

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-002-0513-2

zbMATH Keywords

splinesNewton's methodnumerical examplesquadratic convergenceconvex smoothingbest convex interpolation

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Approximation with constraints (41A29)

Related Items (12)

Smooth and Semismooth Newton Methods for Constrained Approximation and Estimation ⋮ Moreau-Yosida regularization of Lagrangian-dual functions for a class of convex optimization problems ⋮ An augmented Lagrangian method with constraint generation for shape-constrained convex regression problems ⋮ On almost smooth functions and piecewise smooth functions ⋮ Constrained data smoothing via optimal control ⋮ Differentiability and semismoothness properties of integral functions and their applications ⋮ Convergence rate of Newton's method for \(L_2\) spectral estimation ⋮ Armijo Newton method for convex best interpolation ⋮ A smoothing Newton-type method for solving the \(L _{2}\) spectral estimation problem with lower and upper bounds ⋮ Shape-preserving interpolation and smoothing for options market implied volatility ⋮ Computing the Best Approximation over the Intersection of a Polyhedral Set and the Doubly Nonnegative Cone ⋮ Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization

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