The Galahad library is a thread-safe library

Library

In a traditional sense, a library is a large collection of books, and can refer to the place in which the collection is housed. Today, the term can refer to any collection, including digital sources, resources, and services...

 of packages for the solution of optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

—or mathematical programming

Mathematical Programming

Mathematical Programming, established in 1971, and published by Springer Science+Business Media, is the official scientific journal of the Mathematical Optimization Society. It currently consists of two series: A and B. The "A" series contains general publications. The "B" series focuses on topical...

—problems. The areas covered by the library are unconstrained and bound-constrained optimization, quadratic programming

Quadratic programming

Quadratic programming is a special type of mathematical optimization problem. It is the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables....

, nonlinear programming

Nonlinear programming

In mathematics, nonlinear programming is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are...

, systems of nonlinear equations and inequalities, and nonlinear least squares

Least squares

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...

 problems. The library is mostly written in the Fortran 90

Fortran

Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...

 programming language.

The name of the library originates from its major package for general nonlinear programming

Nonlinear programming

In mathematics, nonlinear programming is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are...

, LANCELOT-B, the successor of the original augmented Lagrangian

Augmented Lagrangian method

Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems; the difference is that the augmented Lagrangian...

 package LANCELOT of Conn, Gould and Toint [1].

Other packages in the library include

• a filter-based method for systems of linear and nonlinear equations and inequalities,
• an active-set method for nonconvex quadratic programming
  Quadratic programming
  Quadratic programming is a special type of mathematical optimization problem. It is the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables....
  
  ,
• a primal-dual interior-point method for nonconvex quadratic programming
  Quadratic programming
  Quadratic programming is a special type of mathematical optimization problem. It is the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables....
  
  ,
• a presolver for quadratic programs,
• a Lanczos method for trust-region subproblems,
• an interior-point method to solve linear programs
  Linear programming
  Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
  
   or separable convex programs or alternatively, to compute the analytic center of a set defined by such constraints, if it exists.

Packages in the GALAHAD library accept problems modeled in either the Standard Input Format (SIF) or the AMPL modeling language

AMPL

AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computation AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and...

. For problems modeled in the SIF, the GALAHAD library naturally relies upon the CUTEr

CUTEr

CUTEr is an open source testing environment for optimization and linear algebra solvers...

 package, an optimization toolbox providing all low-level functionalities required by solvers.

The library is available on several popular computing platforms, including Compaq (DEC) Alpha, Cray, HP, IBM RS/6000, Intel-like PCs, SGI and Sun. It is designed to be easily adapted to other platforms. Support is provided for many operating systems, including Digital UNIX, Tru64 UNIX

Tru64 UNIX

Tru64 UNIX is a 64-bit UNIX operating system for the Alpha instruction set architecture , currently owned by Hewlett-Packard . Previously, Tru64 UNIX was a product of Compaq, and before that, Digital Equipment Corporation , where it was known as Digital UNIX .As its original name suggests, Tru64...

, Linux

Linux

Linux is a Unix-like computer operating system assembled under the model of free and open source software development and distribution. The defining component of any Linux system is the Linux kernel, an operating system kernel first released October 5, 1991 by Linus Torvalds...

, HP-UX

HP-UX

HP-UX is Hewlett-Packard's proprietary implementation of the Unix operating system, based on UNIX System V and first released in 1984...

, AIX

AIX operating system

AIX AIX AIX (Advanced Interactive eXecutive, pronounced "a i ex" is a series of proprietary Unix operating systems developed and sold by IBM for several of its computer platforms...

, IRIX

IRIX

IRIX is a computer operating system developed by Silicon Graphics, Inc. to run natively on their 32- and 64-bit MIPS architecture workstations and servers. It was based on UNIX System V with BSD extensions. IRIX was the first operating system to include the XFS file system.The last major version...

 and Solaris

Solaris Operating System

Solaris is a Unix operating system originally developed by Sun Microsystems. It superseded their earlier SunOS in 1993. Oracle Solaris, as it is now known, has been owned by Oracle Corporation since Oracle's acquisition of Sun in January 2010....

, and for a variety of popular Fortran 90

Fortran

Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...

compilers on these platforms and operating systems.

The GALAHAD Library is authored and maintained by N.I.M. Gould, D. Orban and Ph.L. Toint.