On the generation of updates for quasi-Newton methods

DOI10.1007/BF00940567zbMath0563.65037OpenAlexW2015590311MaRDI QIDQ1057625

Jacob Flachs

Publication date: 1986

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00940567

zbMATH Keywords

quasi-Newton methodsJacobian matrixsparsityHessian matrixweighted Frobenius normupdating formulas

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical mathematical programming methods (65K05) Numerical computation of solutions to systems of equations (65H10)

Cites Work

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• A unified derivation of quasi-Newton methods for solving non-sparse and sparse nonlinear equations
• Convergence Theorems for Least-Change Secant Update Methods
• A Sparse Quasi-Newton Update Derived Variationally with a Nondiagonally Weighted Frobenius Norm
• Least Change Secant Updates for Quasi-Newton Methods
• On Variable-Metric Methods for Sparse Hessians
• Continuous Newton-Raphson method for solving and underdetermined system of nonlinear equations
• A note on quasi-newton formulae for sparse second derivative matrices
• A note about sparsity exploiting quasi-Newton updates
• A Unified Derivation of Symmetric Quasi-Newton Update Formulas
• A Generalized Broyden’s Method for Solving Simultaneous Linear Equations
• The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices
• On Sparse and Symmetric Matrix Updating Subject to a Linear Equation
• Minimum Norm Symmetric Quasi-Newton Updates Restricted to Subspaces
• A Family of Variable-Metric Methods Derived by Variational Means
• Variations on Variable-Metric Methods

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