Least-Squares

Release: 1.0

Date: 05 February 2026

Author: Jaroslav Fowkes and Nick Gould

GALAHAD [1] is a suite of open-source routines for large-scale continuous optimization. Currently there is a single package designed to find a local minimizer of a sum-of-squares function whose variables may take any values, a second pair that target linear problems with simple bounds on the variables, another pair for which the feasible region is an intersection of regular simplices, and a final one for which the constraints are linear (polyhedral).

Contents

• BLLS - bound-constrained linear least-squares using a preconditioned, projected-gradient method
• BLLSB - bound-constrained linear least-squares using an interior-point method
• CLLS - linearly-constrained linear least-squares using an interior-point method
• NLS - unconstrained local nonlinear least-squares using a regularization method
• SLLS - simplex-constrained linear least-squares using a preconditioned, projected-gradient method
• SLLSB - simplex-constrained linear least-squares using an interior-point method

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.