Some numerical experiments with variable-storage quasi-Newton algorithms

1989/08/01 by Jean Charles Gilbert, Claude Lemaréchal · 810 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Applied mathematics #Combinatorics #Computer science #Context (archaeology) #Diagonal #Eigenvalues and eigenvectors #Geometry #Hessian matrix #Identity matrix #Initialization #Iterative Methods for Nonlinear Equations #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Newton's method #Nonlinear system #Numerical analysis #Quasi-Newton method #Rank (graph theory) #Variable (mathematics)

paper · open access · doi:10.1007/bf01589113

published in Mathematical Programming 45(1-3), 407-435 (Springer Science+Business Media)

openalex publication_date 1989/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Citations

• On the limited memory BFGS method for large scale optimization
• Optimal conditioning of self-scaling variable Metric algorithms

Cited by

• The AROME-France Convective-Scale Operational Model
• SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
• Data Assimilation and Sensitivity of the Black Sea Model to Parameters
• Convergent least-squares optimisation methods for variational data assimilation
• Practical global oceanic state estimation
• Adjoint accuracy for the full-Stokes ice flow model: limits to the transmission of basal friction variability to the surface
• Recent Observations of Thwaites Glacier, West Antarctica Are Consistent With High Rates of Loss in Next 50 Years
• Pathfinder: Parallel quasi-Newton variational inference
• Algorithm 778: L-BFGS-B
• A New Diagonal Quasi-Newton Updating Method With Scaled Forward Finite Differences Directional Derivative for Unconstrained Optimization
• Optimal Boundary Discretization by Variational Data Assimilation
• Hybridization of colloidal handlebodies with singular defects and topological solitons in chiral liquid crystals
• A Limited Memory Algorithm for Bound Constrained Optimization
• A Dynamic Subspace Based BFGS Method for Large Scale Optimization Problem
• Influences of hydroxyl radicals (OH) on top-down estimates of the global and regional methane budgets
• A Portable and Versatile Limited-Memory BFGS Implementation in PETSc/TAO
• Hessian Initialization Strategies for L-BFGS Solving Non-linear Inverse Problems
• A reduced-order strategy for 4D-Var data assimilation
• Monitoring emissions from the 2015 Indonesian fires using CO satellite data. [europepmc]
• Colloidal interactions and unusual crystallization versus de-mixing of elastic multipoles formed by gold mesoflowers. [europepmc]
• Physical oceanographic factors controlling the ocean circulation-induced magnetic field. [europepmc]