The Galahad library is a

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library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

of packages for the solution of

mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

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

quadratic programming Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constra ...

nonlinear programming In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or sta ...

, systems of nonlinear equations and inequalities, and

non-linear least squares Non-linear least squares is the form of least squares analysis used to fit a set of ''m'' observations with a model that is non-linear in ''n'' unknown parameters (''m'' ≥ ''n''). It is used in some forms of nonlinear regression. The ...

problems. The library is mostly written in the Fortran 90 programming language. The name of the library originates from its major package for general

, LANCELOT-B, the successor of the original augmented Lagrangian package LANCELOT of Conn, Gould and Toint. 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

, * a primal-dual interior-point method for nonconvex

, * a presolver for quadratic programs, * a Lanczos method for trust-region subproblems, * an interior-point method to solve

linear programs Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is ...

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

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and

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, and for a variety of popular Fortran 90 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.

References

External links

* Th
official GALAHAD website
{{Mathematical optimization software Numerical software Mathematical optimization software