# Mathematical Optimization Consultancy

Enabling fast and accurate decision making
What is Mathematical Optimization?

Mathematical Optimization, also known as Mathematical Programming, is an aid for decision making utilized on a grand scale across all industries. Advanced analytical techniques are used to find the best value of the inputs from a given set which is specified by physical limits of the problem and user's restrictions. The quality of the result is measured by a user metric provided as a scalar function of the inputs. Optimization problems come from a massively diverse range of fields and industries, such as portfolio optimization or calibration in finance, structural optimization in engineering, data fitting in weather forecasting, parameter estimation in chemistry and many more.

Building the Mathematical Model

The first step when solving an optimization problem is to build a mathematical model; a mathematical description of the complex system you need to solve. This requires detailed knowledge of the application domain and ideally a good understanding of the applicable solvers.

How can NAG’s Optimization Experts Help?

### Consult, assess, guide, advise, improve, measure = results!

NAG’s optimization experts provide you with all the information needed to solve an optimization problem. They will discuss your current approach and help guide you to use the right solver for the particular problem. If you need to improve the performance, we can assess how your current model fits the particular solver and advise on a possible reformulation or tune the solver for you. If the problem requires it, NAG’s software experts can adapt an existing solver or develop an entirely new one.

## An Example of Global Optimization

Real-life Examples of NAG’s Optimization Consultancy
• Energy & Commodities Trading Company: The client's model was demonstrating unusual behaviour - significant memory footprint and slow convergence. Analysis of the model showed that a more suitable equivalent reformulation was available. When the model was adjusted, the solver performed as expected. The original runtime dropped from 60s to 0.3s, achieving speed up of order 200x.
• Financial Services Software Vendor: An extended site visit by a NAG optimization expert allowed us to discuss the client's problem in greater detail which helped us to identify a weak point within the calculation that was causing convergence issues. We were able to fix this quickly and efficiently.
• Financial Brokerage Company: An existing NAG client contacted NAG Technical Support because he wanted to speed up his class of problems so that they could be solved within a prescribed time limit. After an initial assessment of the problem, a possible solution was identified using recent research from Stanford University for this exact type of problem. A bespoke solution was delivered by NAG’s optimization team during a short consulting engagement. The new solver drastically improved the performance (original runtime of about 4 hours became 2.5 minutes) so that even bigger problems could be considered by the client.
• Oil & Gas Company: NAG’s optimization team helped an Oil & Gas client formulate his gas pipeline problem as a mixed integer linear program (MILP). We then offered a suitable solver and a modelling environment to efficiently solve the problem and its variants - read the full story.
• Major Investment Bank: A NAG optimization expert tweaked the clients solver's options which contributed to the client reducing the memory footprint of the algorithm on his large scale optimization problem. The problem became solvable on his machine.
• Silicon Valley Software Company: This client approached NAG with the specific requirement of adding real time monitoring to their existing NAG optimization solver. The possibilities were discussed and a bespoke implementation of a new solver was created.
• Investment Bank: After assessing this client's optimization problem, a more suitable optimization solver from the NAG Library was suggested. After using the suggested NAG Library solver the client achieved speed-up was of order 100x.
Benefits
Speed & Accuracy Improvements