Abstract
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.
†Dedicated to H. Th. Jongen on the occasion of his 60th birthday.
Acknowledgements
The author would like to thank Prof. Dr Susumu Shindoh for his careful reading of the first version of this manuscript, and the anonymous referees for their helpful comments.
Notes
†Dedicated to H. Th. Jongen on the occasion of his 60th birthday.