Implementing an “exact” Newton method for separable convex transportation problems

Abstract

AbstractConvex transportation problems represent an important special class of convex network flow problems, with particular applications in telecommunications, economics and engineering. This paper describes an implementation of an “exact” Newton algorithm for separable convex transportation problems. Previously in the literature, only approximate Newton algorithms had been described for the general case of convex network flow problems. The special structure of the transportation problem is used to simplify computation of dual multiplier estimates. In general, this would require factorization of a square matrix of dimension n + m − 1, were n is the number of sources and m is the number of sinks. By exploiting structure, the work of factorization is limited to a square matrix of dimension n − 1 or m − 1, whichever is smaller. Some computational experience is described. We also note an analogy between this Newton algorithm for convex problem and a particular variant of Karmarkar's algorithm for linear problems.