Using an interior point method for the master problem in a decomposition approach

We address some of the issues that arise when an interior point method is used to handle the master problem in a decomposition approach. The main points concern the efficient exploitation of the special structure of the master problem to reduce the cost of a single interior point iteration. The particular structure is the presence of GUB constraints and the natural partitioning of the constraint matrix into blocks built of cuts generated by different subproblems. The method can be used in a fairly general case, i.e., in any decomposition approach whenever the master is solved by an interior point method in which the normal equations are used to compute orthogonal projections. Computational results demonstrate its advantages for one particular decomposition approach: Analytic Center Cutting Plane Method is applied to solve large scale nonlinear multicommodity network flow problems (up to 5000 arcs and 10000 commodities).