# Maximize production with new NAG Library Mixed Integer Linear Programming algorithms

Posted OnSeptember 11, 2015 by Geeta Priya

The Numerical Algorithms Group (NAG), numerical software, engineering and HPC service provider, announce new algorithms in the NAG Library for Mixed Integer Linear Programming. The underlying algorithm is a modified Sequential Quadratic Programming (SQP) stabilised by using trust regions and can deal with both convex and nonconvex problems and problems with possibly expensive function evaluations. In addition, it is not assumed that the mixed integer problem has to be relaxable; the function evaluations are requested only at integral points. This is a distinctive feature of the solver since the usual approaches rely on the relaxation of the discrete variables.

Mixed Integer Linear Programming (MILP) problems are defined as those where some or all of the decision variables are only allowed to be integers. This is typically required in a range of real world applications for example, allocation and planning problems where the discrete variables represent quantities, such as the number of individual shares to be held, or the number of pipelines needed or the number of oil-spill cleaning locations to be deployed, and require integer values for the solution. By utilizing tried and trusted NAG MILP algorithms users can improve business planning by maximizing production without exceeding resources when many variables are at play.

Examples of Mixed Integer Linear Programming can be found in many areas including:

• Portfolio optimization

• Design of distribution networks

• Flight path / route / scheduling optimization • Optimal response to catastrophic oil spills • Protein folding

The NAG Library is tried and trusted by users for its quality, depth of coverage, support and documentation. Available for multiple programming languages, environments and platforms that NAG Library is embedded in thousands of applications all over the world. 30 day trials are available on request. Visit www.nag.com <http://www.nag.com> for more information.