Fast Descent Methods for LPs With No Matrix Inversions

Existing software implementations for solving Linear Programming (LP) models are all based on full matrix inversion operations involving every constraint in the model in every step. This linear algebra component in these systems makes it difficult to solve dense models even with moderate size, and it is also the source of accumulating roundoff errors affecting the accuracy of the output. We present new methods for LP that help reduce the need for this linear algebra component significantly, or even eliminate it altogether, and still get comparable or better results.