Use-case: See how derivative-free optimization is used in Macro-economics!

Among the domain of macroeconomics are a series of models called DGSE (Dynamic Stochastic General Equilibrium), that try to explain the effects of economic policies on economic growth. Such models are frequently used by Central Banks to predict global growth of a country.

We studied the Federal Reserve Bank of New York DSGE model implemented in MATLAB using the IRIS toolbox by Iskander Karibzhanov, Senior Scientist at Bank of Canada. This model is highly nonlinear, with no access to exact derivatives. In such cases, one cannot expect the solver to find a solution with as much precision as for a problem for which exact derivatives are provided.

The parallel finite-differencing feature of Artelys Knitro is used to speed up the computation. Using Knitro 11.1 out-of-the-box, the computation time is further decreased by a factor of 5 while achieving the same value of objective value.

A new warm-start option for interior point methods

This version also brings a new option dedicated to warm-start for the two interior point methods embedded in Artelys Knitro (algorithm 1&2). This option allows huge performance improvements when the user is able to provide a good starting point. In addition, models that require solving multiple nonlinear problems sequentially specifically benefit from this new warm-start option. The figure below illustrates a typical application of this new option to solve sequential nonlinear subproblems, the overall computation time is reduced by a factor 10!

Impact of the new warm-start option on the resolution of sequential nonlinear subproblems
Impact of the new warm-start option on the resolution of sequential nonlinear subproblems

Additional features of Artelys Knitro 11.1:

• New Python API with dedicated methods to define structured expressions
• Automatic convexity detection for QP/QCQPs
• Improved Knapsack cut generation including lifted cuts for MINLP problems
• Enhancement of the L-BFGS Hessian approximation
• General performance improvement on convex problems in particular for very large instances