An application of a block iterative method on the primal-dual interior point method

The primal-dual interior point methods have been paid much attention by many researchers. For large scale systems, each problem tends to have a particular structure, and by making use of this special structure, the computational time may well be reduced further. Block angular structure is one of the typical structures on many practical problems. In this paper, a method to reduce computational time required in a primal-dual interior point method on large scale problems with block angular structure is proposed. Furthermore, it is pointed out that the numerical instability may occur when the optimal solutions are degenerate and we propose a method of dealing with it. From the numerical studies on a problem with over 3,000 constraints, the computational time of the proposed method is reduced to about half of the usual implementation. Copyright (C) 1998 IFAC.