Survey of Computational Methods for Solving Large Scale Systems

In recent years computational methods for solving large scale mathematical programming problems have improved enormously. The most fundamental of these improvements have been linear programming, where problems are becoming both larger and more complex in their own right and as sub-problems in non-linear and integer programs. Sophisticated new techniques have enhanced the inversion, pivot selection and updating steps of the simplex algorithm, while generalized upper bounding (GUB) has made possible the solution of some problems of staggering size. In integer and non-convex programming new techniques such as special order sets and pseudo-costs have advanced the art to a stage where problems with a few thousand constraints can be handled with confidence. Similarly improvements in the Method of Approximation Programming (MAP) have made the solution of large and complex non-linear programs computationally attractive. (Author).