Auxiliary Procedures

Release: 1.0

Date: 31 March 2025

Author: Jaroslav Fowkes and Nick Gould

GALAHAD [1] is a suite of open-source routines for large-scale continuous optimization. This is supported by a number of auxiliary procedures that are used to perform commonly-occurring numerical tasks.

Contents

• BSC - build and use the Schur complement from constituent matrices
• CONVERT - convert a sparse matrix from one format to another
• FIT - fit function and derivative values to data
• HASH - set up and use a chained scatter table
• IR - given matrix factors, perform iterative refinement to solve systems
• LHS - compute an array of Latin Hypercube samples
• LMS - maintain limited-memory Hessian approximations
• NODEND - find a row/column ordering for symmetric matrix factorization
• ROOTS - find real roots of real polynomials
• RPD - convert LP/QP data to and from QPLIB format
• SCU - build and extend factors for an evolving block sparse matrix
• SEC - maintain dense BFGS and SR1 secant approximations to a Hessian
• SHA - find a sparse Hessian matrix approximation using componentwise secant approximation
• PRESOLVE - transform LP/QP data so that the resulting problem is easier to solve

References

[1]

Gould, N. I. M., Orban, D., & Toint, Ph. L. (2003). GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Transactions on Mathematical Software (TOMS), 29(4), 353-372.