A “Generalized Product form of Inverse“ Suitable for Large Mathematical Program Partitioning

Abstract

In large Mathematical Program partitionning the fundamental algebraic problem is to revise the inverse of the basis matrix at each step. When the basis is partitionned, the usual Product Form of Inverse (PFl) allows to revise the basis for some steps, but not for all of them. The proposed “Generalized Product Form of Inverse” (GPFl), which includes PFI as a particular case, allows to revise the partitionned basis at any step, so that a partitionned Mathematical Program may be solved exactly as an ordinary Mathematical Program, which may spare a lot of difficulties.The GPFI, which is specially fitted to block angular horizontal mathematical programs, may be particularly efficient with programs having special structures, convex programs, integer programs. Practical examples are given, among which a large integer program partitionned twice, each partition being itself partitionned.