Regularization subproblems

Release: 5.4

Date: Nov 21, 2025

Author: Nick Gould for GALAHAD productions

GALAHAD [1] is a suite of open-source routines for large-scale continuous optimization. Currently there twelve packages designed to find a global minimizer of a variety of regularized quadratic functions

Contents

• TRS - global minization of a quadratic function within an ellipsoid using matrix factorization
• RQS - global minization of a regularized quadratic function using matrix factorization
• TREK - global minization of a quadratic function within an ellipsoid using extended-Krylov-subspace iteration
• NREK - global minization of a regularized quadratic function using using extended-Krylov-subspace iteration
• DPS - global minization of a regularized quadratic function in a diagonalising norm using matrix factorization
• GLTR - global minization of a quadratic function within an ellipsoid using an iterative method
• GLRT - global minization of a regularized quadratic function
• LLSR - global minization of a regularized linear least-squares objective using matrix factorizations
• LLST - global minization of a linear least-squares objective within an ellipsoid using matrix factorizations
• LSTR - global minization of a linear least-squares objective within a sphere using an iterative method
• LSRT - global minization of a regularized linear least-squares objective using an iterative method
• L2RT - global minization of a regularized linear least-Euclidean-norm objective using an iterative 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.