The apex systems past and future

Abstract
A number of features of the APEX-I and/or APEX-III Mathematical Programming Systems that were novel when they were introduced are discussed. These include the use of supersparsity, a numerically stable variant of the Hellerman-Rarick invert, some extensions to matrix reduction algorithms new and methods of model analysis. There is a short discussion of development methodology and overall data structure in the systems. Finally a short discussion of some promising areas of future development is presented.