A Dantzig-Wolfe-like variant of Karmarkar’s interior-point linear programming algorithm

The paper shows that a variant of Karmarkar’s projective algorithm for linear programming can be viewed as following the approach of Dantzig-Wolfe decomposition. At each iteration, the current primal feasible solution generates prices which are used to form a simple subproblem. The solution to the subproblem is then incorporated into the current feasible solution. With a suitable choice of stepsize a constant reduction in potential function is achieved at each iteration. The paper also uses the present analysis to motivate a new primal simplex pivot rule that is closely related to rules used by E. Klotz and L. Schrage.