A discrete Newton algorithm for minimizing a function of many variables

DOI10.1007/BF01583777zbMath0477.90055OpenAlexW2154589350MaRDI QIDQ3934149

Dianne P. O'Leary

Publication date: 1982

Published in: Mathematical Programming (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01583777

zbMATH Keywords

computational complexityconjugate gradientfunction valuesdiscrete Newton algorithmfunction of many variablesgradient values

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Newton-type methods (49M15)

Related Items

Efficient tridiagonal preconditioner for the matrix-free truncated Newton method, A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products, An incomplete Hessian Newton minimization method and its application in a chemical database problem, Numerical techniques in nonparametric estimation†, On the limited memory BFGS method for large scale optimization, Avoiding Modified Matrix Factorizations in Newton-like Methods, Tracing post-limit-point paths with incomplete or without factorization of the stiffness matrix, A matrix-free line-search algorithm for nonconvex optimization, Iterative methods for nonlinear operator equations, Truncated-Newton algorithms for large-scale unconstrained optimization, Block truncated-Newton methods for parallel optimization, Dynamic scaling based preconditioning for truncated Newton methods in large scale unconstrained optimization, The adjoint Newton algorithm for large-scale unconstrained optimization in meteorology applications, Symbiosis between linear algebra and optimization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of Newton-like methods for solving systems of nonlinear equations
• CGS algorithms for unconstrained minimization of functions
• Truncated-Newton algorithms for large-scale unconstrained optimization
• On the Estimation of Sparse Hessian Matrices
• Newton-type methods for unconstrained and linearly constrained optimization
• Solution of Sparse Indefinite Systems of Linear Equations
• A Matrix Modification Method for Calculating Approximate Solutions to Systems of Linear Equations
• A Modified Newton’s Method for Unconstrained Minimization
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Estimates for Some Computational Techniques in Linear Algebra
• On Steepest Descent
• Some Efficient Algorithms for Solving Systems of Nonlinear Equations
• Quasi-Newton Methods for Unconstrained Optimization
• Methods of conjugate gradients for solving linear systems