SYNTHESIS OF COMPACT-INVERSE METHODS FOR BLOCK-ANGULAR LINEAR PROGRAMMING PROBLEMS.

A sequence of partial pivoting operations factors the inverse of a block-angular basis into a very sparse, structured matrix and a block-angular matrix. Using this product form of the inverse in the (revised) simplex method yields H. Mueller- Merbach's direct decomposition method, which is shown to be equivalent to generalized upper bounding. Using it in the dual simplex method yields either J. B. Rosen's partitioning method or D. Ohse's dual direct decomposition method, depending on how the pivot row is selected. A bound on the number of multiplications per iteration is given for each method and compared with the bounds for the revised simplex and dual revised simplex methods without the product form of the inverse.