On the Complexity of a Linear Programming Predictor-Corrector Algorithm Using the Two Norm Neighborhood

In this work the complexity of a feasible variant of a Linear Programming Predictor-Corrector algorithm specialized for transportation and assignment problems is explored. A O(n| log(epsilon)|) iteration complexity was achieved by proving that the step size computed by the studied algorithm is bounded at each iteration by theta(4-3 theta)(1-theta)(2)/n, where theta is an element of [0, 1[. Therefore, allowing to conclude that the analyzed Predictor-Corrector algorithm that uses the 2-norm neighborhood has polynomial iteration complexity and is Q-linearly convergent.