Interior Point Methods With Decomposition For Linear Programs

This paper deals with an algorithm which incorporates the interior point method into the Dantzig-Wolfe decomposition technique for solving large-scale linear programming problems. At each iteration, the algorithm performs one step of Newton's method to solve a subproblem, obtaining an approximate solution, which is then used to compute an approximate Newton direction to nd a new vector of the Lagrange multipliers. We show that the algorithm is globally linearly convergent and has the polynomial-time complexity.