On diagonally structured problems in unconstrained optimization using an inexact super Halley method

DOI10.1016/j.cam.2011.07.006zbMath1256.65055OpenAlexW2128699861MaRDI QIDQ432797

Geir Gundersen, Trond Steihaug

Publication date: 4 July 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.07.006

zbMATH Keywords

numerical examplesiterative methodconjugate gradient methodHalley's methodinexact Newton methodtruncated Newton methodChebyshev's methodlarge scale unconstrained optimization

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10)

Related Items (2)

A new class of root-finding methods in \({\mathbb {R}}^n\): the inexact tensor-free Chebyshev-Halley class ⋮ Higher-order reverse automatic differentiation with emphasis on the third-order

Uses Software

• LANCELOT
• ITSOL
• ve08
• SPARSKIT

Cites Work

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• On the method of tangent hyperbolas in Banach spaces
• Parallel solution of linear systems with striped sparse matrices
• A local convergence theorem for the super-Halley method in a Banach space
• Historical developments in convergence analysis for Newton's and Newton-like methods
• Rate of convergence of higher-order methods
• Sparsity in higher order methods for unconstrained optimization
• Truncated-Newton algorithms for large-scale unconstrained optimization
• On the Halley class of methods for unconstrainedoptimization problems
• On large-scale unconstrained optimization problems and higher order methods
• Inexact Newton Methods
• Some Numerical Results Using a Sparse Matrix Updating Formula in Unconstrained Optimization
• A family of Chebyshev-Halley type methods in Banach spaces
• Theoretical efficiency of a new inexact method of tangent hyperbolas
• An acceleration of Newton's method: Super-Halley method

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