New Optimization Routines added to the NAG Optimization Modelling Suite

The latest Mark of the NAG Library features even more Optimization routines to enhance computing and instruction

New routines include: a derivative free solver for nonlinear least squares subject to bound constraints and an interior point method for large scale linear programming problems

12 October 2017 - The Numerical Algorithms Group (NAG), experts in algorithms, software and HPC announce additional Optimization solvers in a new release of the NAG Library. NAG continues to focus on their highly popular Optimization Chapter, and with the expansion of their Optimization Team in 2016, users of the NAG Library are seeing exciting new content continue to be developed and released.

Mark 26.1 of the Library sees two new Optimization routines added to the NAG Optimization Modelling Suite within the NAG Library – Derivative-free Optimization for Data Fitting and an Interior Point Method for Large Scale Linear Programming Problems.

The Derivative-free Optimization for Data Fitting solver was developed in collaboration with the Centre for Doctoral Training in Industrially Focused Mathematical Modelling (InFoMM) at the University of Oxford. Calibrating the parameters of complex numerical models to fit real world observations is one of the most common problems found in many applications such as finance, multi-physics simulations and engineering. It is not easy, or even possible to evaluate derivatives of functions which appear in the optimization model and thus many well-established approaches in mathematical optimization might not be satisfactory. Moving to a derivative-free regime presents novel approaches for approximating the solution without computing or estimating derivatives. NAG added its first derivative-free solver to the NAG Library approximately five years ago. Since then this field has attracted significant academic attention, resulting in numerous advances. The new Mark 26.1 Derivative-free Optimization Solver can effectively exploit the structure of calibration problems and is thought to be the first such commercial solver publicly available in the world.

The second Optimization routine is an Interior Point Method for Large Scale Linear Programming Problems built upon a very efficient sparse linear algebra package and implements two variants of interior point methods: The Primal-Dual and Self-Dual methods. The Primal-Dual usually offers the fastest convergence and is the solver of choice. Both implementations should present significant speed-ups for large scale problems over the current LP/QP solvers in the Library. Linear programming is popular in finance and logistics, particularly optimizing planning, production and transportation processes, but also lends itself to many other fields and industries.


The NAG Optimization Modelling Suite was developed to better tackle the input of complex problems without forming difficult interfaces with a daunting number of arguments. It is available for the two new optimization solvers mentioned above (26.1), and the semidefinite programming solver and the interior point method for nonlinear optimization introduced at Mark 26.

An additional 20 other numerical routines are also new to the Library at Mark 26.1. Learn more about the new functionality.