An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming is discussed. We consider the general convex program formulated in the conic form. For the problem, we define the perturbed Lagrangian relaxation by using the self-concordant barriers, and show the basic properties of the perturbed problems. Based on the properties, we present a conceptual method which numerically traces the trajectory that leads to the optimal solution of the original problem.