GALAHAD Julia Interfaces

Release: 1.0

Date: Jun 19, 2024

Author: Jaroslav Fowkes, Nick Gould, Alexis Montoison and Dominique Orban

GALAHAD [1] is a suite of open-source routines for large-scale continuous optimization. GALAHAD 4.2 and above provides Julia functions that link transparently to the underlying fortran.

Contents

• Unconstrained Optimization
  • ARC - unconstrained local optimization of a smooth function using a regularization method
  • TRU - unconstrained local optimization of a smooth function using a trust-region method
• Bound-constrained Optimization
  • TRB - bound-constrained local optimization of a smooth function
• Least-Squares
  • 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
• Linear Programming
  • LPA - linear programming using the simplex method
  • LPB - linear programming using an interior-point method
  • WCP - find a well-centered point within a polyhedral set
• Quadratic Programming
  • BQP - bound-constrained quadratic programming using a preconditioned, projected-gradient method
  • BQPB - bound-constrained quadratic programming using an interior-point method
  • CQP - convex quadratic programming using an interior-point method
  • CRO - crossover from an interior-point to basic solution for convex quadratic programming
  • DQP - convex quadratic programming using a dual active-set method
  • EQP - equality-constrained quadratic programming using an iterative method
  • LSQP - linear or separable convex quadratic programming using an interior-point trust-region method
  • QPA - non-convex quadratic programming using an active-set method
  • QPB - non-convex quadratic programming using an interior-point method
• Regularization subproblems
  • TRS - global minization of a quadratic function within an ellipsoid using matrix factorization
  • RQS - global minization of a regularized quadratic function using matrix factorization
  • 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
• Linear Systems
  • SLS - solve symmetric systems of linear equations (übersolver)
  • ULS - solve unsymmetric systems of linear equations (übersolver)
  • SBLS - precondition and solve block symmetric systems of linear equations
  • PSLS - precondition symmetric, positive-definite systems of linear equations (übersolver)
  • SILS - solve symmetric systems of linear equations
  • GLS - solve unsymmetric systems of linear equations
  • FDC - find an equivalent linearly independent subset of a system of linear equations
• Global Optimization
  • UGO - univariate global optimization of a smooth function over an interval
  • BGO - multivariate global optimization of a smooth function within a box using stochastic methods
  • DGO - multivariate global optimization of a smooth function within a box using deterministic methods
• Auxiliary Procedures
  • 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
  • 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

• Index

• Search Page

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.