Implementing Interior Point Linear Programming Methods in the Optimization Subroutine Library

This paper discusses the implementation of interior point (barrier) methods for linear programming within the framework of the IBM Optimization Subroutine Library. This class of methods uses quite different computational kernels than the traditional simplex method. In particular, the matrices we must deal with are symmetric and, although still sparse, are considerably denser than those assumed in simplex implementations. Severe rank deficiency must also be accommodated, making it difficult to use off-the-shelf library routines. These features have particular implications for the exploitation of the newer IBM machine architectural features. In particular, interior methods can benefit greatly from use of vector architectures on the IBM 3090™ series computers and “super-scalar“ processing on the RISC System/6000™ series.