Optimization Software for Semidefinite Programming
NAG closely collaborates with the Optimization Group from University of Birmingham led by Professor Michal Kocvara (http://web.mat.bham.ac.uk/kocvara/).
One of the outcomes of the collaboration will be a set of new routines in the NAG Libraries based on the Pennon optimization package (http://web.mat.bham.ac.uk/kocvara/pennon/).
Pennon (PENalty method for NONlinear and semidefinite programming) is based on a generalized augmented Lagrangian method. Its uniqueness lies in a special penalty/barrier function which allows it to handle generic matrix inequalities side by side with nonlinear constraints. One can solve problems such as linear semidefinite programming problems (SDP) or formulations with bilinear matrix inequalities (BMI) as well as fully nonlinear semidefinite programming problems (NLP-SDP).
The code exploits sparse data structures and is aimed at large-scale problems. Such problems arise in many fields including structural optimization, control theory or finance. The first new routines are planned for the next release of the NAG Library.
We are also working on a new project which is an extension to Pennon to cover SOCP (Second Order Conic Programming) problems.