A chordal preconditioner for large-scale optimization

DOI10.1007/BF01580736zbMath0685.90085MaRDI QIDQ1262220

Thomas F. Coleman

Publication date: 1988

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

zbMATH Keywords

Cholesky factorizationchordal graphHessian matrixsmooth functionlarge sparse numerical optimizationautomatic preconditioning schemeblock-diagonal approximationgraph- theoretic heuristiclinear conjugate-gradient algorithmperfect elimiation graph

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Nonlinear programming (90C30)

Related Items

A vertex incremental approach for maintaining chordality, Maximal sub-triangulation in pre-processing phylogenetic data, A direct active set algorithm for large sparse quadratic programs with simple bounds

Uses Software

• LINPACK
• symrcm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large sparse numerical optimization
• Maximal chordal subgraphs
• Estimation of Sparse Jacobian Matrices and Graph Coloring Blems
• Optimization of unconstrained functions with sparse hessian matrices-newton-type methods
• Software for estimating sparse Jacobian matrices
• The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
• Estimation of sparse hessian matrices and graph coloring problems
• An Incomplete Factorization Technique for Positive Definite Linear Systems
• On the Estimation of Sparse Hessian Matrices
• Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients
• Algorithmic Aspects of Vertex Elimination on Graphs
• Some Numerical Results Using a Sparse Matrix Updating Formula in Unconstrained Optimization
• A class of first order factorization methods
• A comparasion of three resequencing algorithms for the reduction of matrix profile and wavefront
• The Cyclic Coloring Problem and Estimation of Sparse Hessian Matrices
• On the Successive Projections Approach to Least-Squares Problems
• A New Algorithm for Unconstrained Optimization