AN APPROACH TO LARGE-SCALE NON-LINEAR PROGRAMMING

Due to changing matrix elements, many of the computational benefits embodied in sparse matrix theory and implemented in commercial LP codes for maintaining a sparse matrix inverse updates are lost for NLP. This study reports on the results of investigating the use of structural decomposition in large, sparse NLP problems using the GRG (Generalized Reduced Gradient) algorithm. The approach is to partition the basis matrix into block lower triangular (BLT) form. At each step of the GRG algorithm, all operations are based upon the smallest diagonal subsets of variables. This approach led to the development of an algorithm to dynamically order a square matrix into block, lower triangular form after a column replacement. The method is fast, showing computational time reductions of up to a factor of 10 over performing the ordering on the complete occurrence matrix, while requiring a minimal amount of computer memory. This work it pertinent to chemical engineering optimization.