USING AN INTERIOR-POINT METHOD FOR THE MASTER PROBLEM IN A DECOMPOSITION APPROACH

We addres 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 structur e 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 bui lt 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 re sults demonstrate its advantages for one particular decomposition. app roach: Analytic Center Cutting Plane Method (ACCPM) is applied to solv e large scale nonlinear multicommodity network flow problems (up to 50 00 arcs and 10000 commodities), (C) 1997 Elsevier Science B.V.