Both experts and novices can benefit from computer assistance if something goes wrong, but until recently, very few appropriate tools have been available. The real barrier in mathematical programming is no longer the actual solution of the model. Now the barrier is the correct design, formulation, debugging, and communication of large and complex models. I am working towards providing software tools that mathematical programmers can use to break through this barrier. One major thrust in this area has been the analysis of infeasible models.
Further research is needed.
One class of infeasibility analysis algorithms can be directly applied to the problem of classifying data, the same task performed by neural networks. See below for more information. A second major thrust has been the development of general-purpose tools for the analysis of mathematical programs. Many optimization problems that arise in business and industry are extremely hard to solve because they involve integer-valued variables or nonlinear relationships, or both simultaneously. Better solution algorithms are needed, and will of great commercial value.