Exploiting special structure in a primal-dual path-following algorithm

A primal-dual path-following algorithm that applies directly to a linear program of the form, min{c^tx{divides}Ax = b, Hx ≤u, x ≥ 0, x ∈ ℝⁿ}, is presented. This algorithm explicitly handles upper bounds, generalized upper bounds, variable upper bounds, and block diagonal structure. We also show how the structure of time-staged problems and network flow problems can be exploited, especially on a parallel computer. Finally, using our algorithm, we obtain a complexity bound of O( {Mathematical expression}ds² log(nk)) for transportation problems with s origins, d destinations (s <d), and n arcs, where k is the maximum absolute value of the input data.