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.

Real-life Examples of NAG 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.
Problem solved and performance gained

“The help that NAG provided was invaluable for us. The increase in speed that we are now able to achieve, when solving our specific pipeline problem, was amazing and the knowledge we were given about optimization solvers, problem formulation and modelling techniques was more than we hoped for. The NAG people are a pleasure to work with and I couldn’t have wished for more from any consultancy engagement.” 

Michael Krätsch, PSI

Modern modelling techniques in convex optimization and its applicability to finance and beyond

Convex optimization, particularly Second-order Cone Programming (SOCP) and Quadratically Constrained Quadratic Programming (QCQP), saw a massive increase of interest thanks to robustness and performance. A key issue is to recognize what models can be reformulated and solved using these optimization methods. This webinar introduces the background of SOCP and QCQP, and reviews basic and more advanced modelling techniques. These techniques are demonstrated in real-world examples in Portfolio Optimization.

Consultancy Benefits

Speed & Accuracy Improvements

  • Speed and/or accuracy improvements are common benefits from using the right optimization solver. A special structure in your problem can be exploited by a tailored solution/solver

Deliver Competitive Advantage

  • Our focus on the solvers combined with yours on your application delivers cutting edge functionality and competitive advantage
Credentials - Why NAG?

NAG has been developing numerical software for nearly 50 years. Our optimization experts develop and maintain the extensive collection of optimization solvers in the NAG Library. The experience gained from developing, supporting, documenting and maintaining the algorithms plus helping to solve real-life optimization problems means the team is well equipped to tackle projects across industry and discipline. If you have a problem that could benefit from expert analysis and advice, contact us.